Journal Vol – 13 No -2, June 2018

Abstract:

In this article, we consider the space-time fractional coupled modified Korteweg-de-Vries (mKdV) equations and the space-time fractional coupled Whitham-Broer-Kaup (WBK) equations which are important mathematical model to depict the propagation of wave in shallow water under gravity, combined formal solitary wave, internal solitary waves in a density and current stratified shear flow with a free surface, ion acoustic waves in plasma, turbulent motion, quantum mechanics and also in financial mathematics. We examine new, useful and further general exact wave solutions to the above mentioned space-time fractional equations by means of the generalized -expansion method by using of fractional complex transformation and discuss the examined results with other method. This method is more general, powerful, convenient and direct and can be used to establish new solutions for other kind nonlinear fractional differential equations arising in mathematical physics. Keywords: Coupled mKdV equations; coupled WBK equation; nonlinear evolution equations; fractional differential equations.

Keywords:

Coupled mKdV equations, coupled WBK equation,nonlinear evolution equations,ractional differential equations,

Refference:

I.Alam, M.N. and Akbar, M.A. “The new approach of the generalized -expansion method for nonlinear evolution equations”. Ain Shams Eng. J., Vol. 5, pp 595-603 (2014).

II.Alam, M.N. and Akbar, M.A. “Application of the new approach of generalized )/(GG-expansion method to find exact solutions of nonlinearPDEs in mathematical physics”. BIBECHANA, Vol. 10, pp 58-70 (2014).

III.Ahmad, J., Mushtaq, M. and Sajjad, N. “Exact solution of Whitham-Broer-Kaup shallow water equations”. J. Sci. Arts, Vol. 1, No. 30, pp 5-12 (2015).

IV.Ali, A.H.A “The modified extended tanh-function method for solving coupled mKdV and coupled Hirota-Satsuma coupled KdV equations”. Phys. Lett. A, Vol. 363, No. (5-6), pp 420-425 (2007).

V.Atchi, L.M. and Appan, M.K., “A Review of the homotopy analysis method and its applications to differentialequations of fractional order”.Int. J. Pure Appl. Math., Vol. 113, No. (10), pp 369-384 (2017).

VI.Bekir, A. and Guner, O. “Exact solutions of nonlinear fractional differential equation by -expansion method”. Chin. Phys. B, Vol. 22, No. (11), pp 1-6 (2013).

VII.Bekir, A., Kaplan, M. “Exponential rational function method for solving nonlinear equations arising in various physical models”. Chin. J. Phys.54(3), 365–370(2016).

VIII.Bulut, H. Baskonus, H.M. and Pandir, Y. “The modified trial equation methodfor fractional wave equation and time fractional generalized Burgers equation”. Abst. Appl. Anal., 2013, Article ID 636802, (2013).

IX.Caputo, M. and Fabrizio, M.A. “A new definition of fractional derivatives without singular kernel”. Math. Comput. Model., Vol. 1, pp. 73-85 (2015).

X.Deng, W. “Finite element method for the space and time fractional Fokker-Planck equation”.Siam J. Numer. Anal., Vol. 47, No. (1), pp 204-226 (2009).

XI.Ege, S.M. and Misirli, E. “Solutions of space-time fractional foam drainage equation and the fractional Klein-Gordon equation by use of modified Kudryashov method”.Int. J. Res. Advent Tech., Vol. 2, No. (3), pp 384-388 (2014).

XII.El-Sayed, A.M.A., Behiry, S.H. and Raslan, W.E. “The Adomin’s decomposition method for solving an intermediate fractional advection-dispersion equation”. Comput. Math. Appl., Vol. 59, No. (5), pp 1759-1765 (2010).

XIII.El-Borai, M.M., El-Sayed, W.G. and Al-Masroub, R.M. “Exact solutions for time fractional coupled Whitham-Broer-Kaup equations via exp-function method”.Int. Res. J. Eng. Tech., Vol. 2, No. (6), pp 307-315 (2015).

XIV.Gomez-Aguilar, J.F., Yepez-Martnrez, H., Escober-Jimenez, R.F., Olivarer-Peregrino, V.H., Reyes, J.M. and Sosa, I.O. “Series solution for the time-fractional coupled mKdV equation using the homotopy analysis method”. Math. Prob. Eng., Vol. 2016, Article ID 7047126, 8 pages2016.

XV.He, J.H., Elagan, S.K. and Li, Z.B. “Geometrical explanation of the fractional complex transform and derivative chain rule for fractional calculus”. Phys. Lett. A, Vol. 376, No. (4), pp 257-259 (2012).

XVI.He, J.H. “Asymptotic methods for solitary solutions and compacts”. Abst. Appl. Anal., Volume2012, Article ID916793, 130 pages(2012).

XVII.Helal, M.A. and Mehanna, M.S. “The tanh-function method and Adomin decomposition method for solving the foam drainage equation”. App. Math. Comput., vol. 190, No. (1), 599-609 (2007).

XVIII.Inc, M. “The approximate and exact solutions of the space and time-fractional Burgers equations with initial conditions by the variational iteration method”. J. Math. Anal. Appl., Vol. 345, No. (1), pp 476-484 (2008).

XIX.Jumarie, G. “Modified Riemann-Liouville derivative and fractional Taylor series of non-differentiable functions further results”. Comput. Math. Appl., Vol. 51, No. (9-10), pp. 1367-1376 (2006).

XX.Kadem, A. and Baleanu, D. “On fractional coupled Whitham-Broer-Kaup equations”. Rom. J. Phys., Vol. 56, No. (5-6), pp 629-635 (2011).

XXI.Kaplan, M. Bekir, A. Akbulut, A. and Aksoy, E. “The modified simple equation method for nonlinear fractional differential equations”. Rom. J. Phys., Vol. 60, No. (9-10), pp 1374-1383 (2015).

XXII.Lu, B. “Backlund transformation of fractional Riccati equation and its applications to nonlinear fractional partial differential equations”.Phys. Lett. A, Vol. 376, pp 2045-2048 ( 2012).

XXIII.Lu, B. “The first integral method for some time fractional differential equations”. J. Math. Appl., Vol. 395, pp. 684-693 (2012).

XXIV.Lu, D., Yue, C. and Arshad, M. “Traveling wave solutions of space-time fractional generalized fifth-order KdV equation”. Advances Math. Phys., Volume 2017, Article ID 6743276, 6 pages, (2017).

XXV.Moatimid, G.M., El-Shiekh, R.M., Ghani, A. and Al-Nowehy, A.A.H. “Modified Kudryashov method for finding exact solutions of the (2+1) dimensional modified Korteweg-de Varies equations and nonlinear Drinfeld-Sokolov system”. American J. Comput. Appl. Math., Vol. 1, No. 1 (2011).

XXVI.Odibat, Z. and Monani, S. “The variational iteration method: An efficient scheme for handling fractional partial differential equations in fluid mechanics”. Coumpt. Math. Appl., Vol. 58, No. (11-12), pp 2199-2208 (2009).

XXVII.Rabtah, A.A., Erturk, R.S. and Momani, S. “Solution of fractional oscillator by using differential transformation method”.Comput. Math. Appl., Vol. 59, pp 1356-1362 (2010).

XXVIII.Saad, M.,Ehgan, S.K.,Hamed, Y.S. and Sayed, M. “Using a complex transformation to get an exact solution for fractional generalized coupled mKdV and KDV equations”.Int. J. Basic Appl. Sci., Vol. 13, No. (01), pp 23-25(2014).

XXIX.Wang, G.W. and Xu, T.Z. “The modified fractional sub-equation method and its applications to nonlinear fractional partial differential equations”.Rom. J. Phys., Vol. 59, No. (7-8), pp 636-645 (2014).

XXX.Yan, Z. and Zhang, H. “New explicit solitary wave solutions and periodic wave solutions for Whitham-Broer-Kaup equations in shallow water”. Phys. Lett. A, Vol. 285, No. (5-6), pp 355-362 (2001).

XXXI.Yepez-Martinez, H., J.M. Reyes and I.O. Sosa, “Fractional sub-equation method and analytical solutions to the Hirota-Satsuma coupled KdV equation and mKdv equation”. British J. Math. Coumpt. Sci., Vol. 4, No. (4), pp 572-589 (2014).

XXXII.Younis, M. “The first integral method for time-space fractional differential equations”. J. Adv. Phys., Vol. 2, pp 220-223 (2013).

XXXIII.Younis, M. and Zafar, A. “Exact solutions to nonlinear differential equations of fractional order via -expansion method”. Appl. Math., Vol. 2014, No. (5), pp 1-6 (2014).

XXXIV.Zayed, E.M.E, Amer, Y.A. and Al-Nowehy, A.G. “The modified simple equation method and the multiple ex-function method for solving nonlinear fractional Sharma-Tasso-Olver equation”. Acta Mathematicae Applicatae Sinica, English Series, Vol. 32, No. (4), pp 793-812 (2016).

XXXV.Zayed, E.M.E., Amer, Y.A and Shohib, R.M.A. “The fractional complex transformation for nonlinear fractional partial differential equations in the mathematical physics”. J. Association Arab Uni. Basic Appl. Sci., Vol. 19, pp 59-69 (2016).

XXXVI.Zheng, B. “Exp-function method for solving fractional partial differential equations”.Sci. World J., DOI: 10.1155/2013/465723(2013).

XXXVII.Zheng, B. and Feng,Q. “The Jacobi elliptic equation method for solving fractional partial differential equations”.Abst. Appl. Anal.,2014, 9 pages, Article ID249071(2014).

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Abstract:

Selection of Relay for unlicensed transmission in cooperation based cognitive radio systems is an essential area of research which ensures the transmission performance of the secondary system & at the same time maintains the transmission behavior of the licensed network with respect to the quality-of-service (QoS).So far we have studied Signal-to-Interference-plus-Noise Ratio (SINR) of a relay node as the sole parameter to judge the BEST relay in the existing research works. This time we have proposed few other important parameters like Reliability and Relative Link Quality (RLQ) of a relay node as seen from the receiver, in order to select the Reliable BEST relay in a more accurate manner from the rest of the lot as the authors believe that for a faithful transmission, the selected best relay should be reliable along with other parameters. We have carried out ample simulation study to find out the reliable best relay applying our proposed fuzzy logic-based scheme. The implementation of the suggested system is verified with the earlier proposed schemes, i.e., fuzzy logic-based, SINR based and without relay have been studied holistically through the Secondary Outage Probability & Bit Error Rate (BER) simulation results. Keywords : Best Relay selection, Relay node, Cognitive radio Systems, Decision making, Fuzzy logic.

Keywords:

Best Relay selection,Relay node,Cognitive radio Systems,Decision making, Fuzzy logic,

Refference:

I. Akyildiz, I. F.; Wang, X. andWang, W. “Wireless mesh networks: a survey”.Computer networks, 47(4), pp 445-487 (2005).

II.Akyildiz, I. F.; et. al. “CRAHNs: Cognitive radio ad hoc networks”. Ad Ho Networks, 7(5), pp 810-836(2009).

III. Beres, E. andAdve, R. “Selection cooperation in multi-source cooperative networks”. IEEE Transactions on Wireless Communications, 7(1)(2008).

IV. Banerjee J.S.;Chakraborty A and Chattopadhyay A.“Fuzzy Based Relay Selection for Secondary Transmission in Cooperative Cognitive Radio Networks”. In: Proc. OPTRONIX, Springer,pp 279-287 (2017).

V. Banerjee J.S.; Chakraborty A and Chattopadhyay A. “Relay node selection using analytical hierarchy process (AHP) for secondary transmission in multi-user cooperative cognitive radio systems”. In: Proc. ETAEERE, Springer, pp 745-754 (2018).

VI. Chakraborty, A.; Banerjee, J. S. andChattopadhyay, A. “Non-Uniform Quantized Data Fusion Rule Alleviating Control Channel Overhead for Cooperative Spectrum Sensing in Cognitive Radio Networks”. In: Proc. IACC, pp 210-215(2017).

VII.FCC (2003).ET Docket No 03-222 Notice of proposed rule making and order.VIII.Gao, X.; Wu, G. andMiki, T. “End-to-end QoS provisioning in mobile heterogeneous networks”.Wireless Communications, IEEE, 11(3), pp 24-34(2004).

IX. Jing, T.; Zhu, S.; Li, H.; Xing, X.; Cheng, X.; Huo, Y.; … andZnati, T. “Cooperative relay selection in cognitive radio networks”. IEEE Transactions on Vehicular Technology, 64(5), pp 1872-1881(2015).

X. Kandukuri, S. andBoyd, S. “Optimal power control in interference-limited fading wireless channels with outage-probability specifications”. IEEE transactions on wireless communications, 1(1), pp 46-55(2002).

XI. Laneman, J. N.; Tse, D. N. andWornell, G. W. “Cooperative diversity in wireless networks: Efficient protocols and outage behavior”. IEEE Transactions on Information theory, 50(12), pp 3062-3080(2004).

XII.Mitola, J. andMaguire Jr, G. Q. “Cognitive radio: making software radios more personal”. IEEE Personal Communications, 6(4), pp 13-18(1999).

XIII.Mitola,J. III.”Cognitive Radio—An Integrated Agent Architecture for Software Defined Radio”. Sweden: Royal Institute of Technology,(2000).

XIV. Paul S.; et. al. “A Fuzzy AHP-Based Relay Node Selection Protocol for Wireless Body Area Networks (WBAN)”. In: Proc. OPTRONIX 2017 (Press), IEEE, Nov. (2017).

XV. Paul S.; et. al.“The Extent Analysis Based Fuzzy AHP Approach for Relay Selection in WBAN”. In: Proc. CISC (Press), AISC-Springer, (2018).

XVI. Saha O.; Chakraborty A. and Banerjee J. S. “A Decision Framework of IT-Based Stream Selection Using Analytical Hierarchy Process (AHP) for Admission in Technical Institutions”. In: Proc. OPTRONIX 2017 (Press), IEEE, Nov. (2017).

XVII. Saha O.;Chakraborty A. and Banerjee J.S.: A Fuzzy AHP Approach to IT-Based Stream Selection for Admission in Technical Institutions in India. In: Proc. IEMIS (Press), AISC-Springer, (2018).

XVIII.Simeone, O.; Gambini, J.; Bar-Ness, Y. andSpagnolini, U. “Cooperation andcognitiveradio”. In ICC,IEEE, pp6511-6515(2007)

XIX.Zou, Y.; Zhu, J.; Zheng, B.; Tang, S. andYao, Y. D. “A cognitive transmission scheme with the best relay selection in cognitive radio networks”. In GLOBECOM,IEEE, pp 1-5 (2010).

XX.Zhang, Q.; Jia, J. andZhang, J. “Cooperative relay to improve diversity in cognitive radio networks”. IEEE Communications Magazine, 47(2), pp 111-117(2009)

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Abstract:

Abstract The development of prosthetic arm in accordance with the stable control mechanism is the blooming field in the engineering study. The analysis of Model Reference Adaptive Control (MRAC) for Prosthetic arm utilizing Gradient method MIT rule has been presented using controlling system parameters of the D.C motor. Adaptive tuning and performance analysis has been done for controlling hand prosthesis system using Adaptive I-PD controller constraints rationalized time to time in response with variations in D.C motor parameters to track the desired reference model and application of Gradient Method MIT-Rule. Further on, Lyapunov rule has been implemented towards closed loop asymptotic tracking to ensure global stability on nonconformity of plant parameters because adaptive controller design based on MIT rule doesn’t guarantee convergence or stability. Computer-aided control system design (CACSD) and analysis has been done using MATLAB-Simulink towards adaptive controller design and estimation of adaptation gain.  

Keywords:

Mechanical Prosthetic Arm,Model Reference Adaptive Control(MRAC),Adaptive I-PD control,Gradient method MIT rule,Lyapunov rule,

Refference:

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III.Boonsrimuang P., NumsomranA.andKangwanrat S,“ Design of PI Controller Using MRAC Techniques For Couple-Tanks Process” World Academy of Science, Engineering and Technology International Journal of Mechanical, Aerospace, Industrial, Mechatronic and Manufacturing Engineering Vol:3, No:11, 2009.

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V.Dan Zhang, Bin Wei “Convergence performance comparisons of PID, MRAC, and PID + MRAC hybrid controller” Higher Education Press and Springer-Verlag Berlin Heidelberg 2016.

VI.Engeberg ED. Human model reference adaptive control of a prosthetic hand.J Intel Robot Syst. 2013.

VII.Hans Butler, GerHonderd, and Job van Amerongen “Model Reference Adaptive Control of a Direct-Drive DC Motor” IEEE Control Systems Magazine, doi: 0‟272-170818910100-0

VIII.Jen-Hsing Li and Juing-ShianChiou “GSA-Tuning IPD Control of a Field-Sensed Magnetic Suspension System” Sensors 2015, 15, 31781–31793; doi:10.3390/s151229879

IX.Manabu Kano, Kenichi Tasaka, Morimasa Ogawa, Shigeki Ootakara,AkitoshiTakinami, Shinichi Takahashi, and Seiji Yoshii “Practical Direct PID/I-PD Controller Tuning and Its Application to Chemical Processes” 2010 IEEE International Conference on Control Applications Part of2010 IEEE Multi-Conference on Systems and Control Yokohama, Japan, September 8-10, 2010.

X.Oltean, S.E. and Morar, A. (2010) „Simulation of the local model reference adaptive control of the robotic arm with DC motor drive‟, ACTA Electrotechnica, Vol. 51, No. 2, pp.114–118.

XI.OrieBassey O. “Construction of Lyapunov Functions For Some Fourth Order Nonlinear Ordinary Differential Equations By Method Of Integration” International Journal of Scientific & Technology Research Volume 3, Issue 10, October 2014.

XII.Prof.Nasar A, Dr. N E Jaffar and Sherin A KochummenLyapunov Rule Based Model Reference Adaptive Controller Designs ForSteam Turbine Speed. International Journal of Electrical Engineering &Technology, 6(7), 2015, pp. 13-22.

XIII.Ramadan A. Elmoudi, Mustafa R. Abuzeid, and Nasr E. Shtawa, “Speed Control of DC Motor Based on Model Reference Adaptive Controller,” Al-Azhar University Engineering Journal, JAUES Vol. 2, No. 5 Apr. 2007.

XIV.S. J. Suji Prasad, Susan Varghese, P. A. Balakrishnan “Particle Swarm Optimized I-PD Controller for Second Order Time Delayed System” International Journal of Soft Computing and Engineering (IJSCE) ISSN: 2231-2307, Volume-2, Issue-1, March 2012.

XV.S.Coman., and Cr.Boldisor., “ Adaptive PI controller design to control a mass-damper-spring process.” Bulletin of the Transilvania University of Braşov • Series I • Vol. 7 (56) No. 2 –2014.

XVI.Sumit Kumar Sar, Lillie Dewan “MRAC Based PI Controller for Speed Control of D.C. Motor Using Lab View” WSEAS Transactions On Systems And Control.

XVII.Taifour Ali, EisaBashier, Omar BusatialzainMohd “Adaptive PID Controller for Dc Motor Speed Control,” International Journal of Engineering Inventions, September 2012.

XVIII.V. Rajinikanth and K. Latha “I-PD Controller Tuning for Unstable System Using Bacterial Foraging Algorithm: A Study Based on Various Error Criterion”Hindawi Publishing Corporation Applied Computational Intelligence and Soft ComputingVolume 2012, Article ID 329389.

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Abstract:

Abstract In this paper, the analytical solutions to the space-time fractional modified Benjamin-Bona-Mahony (mBBM) equation involving conformable fractional derivative in science and engineering are examined by using the proposed fractional generalized (D G/G)-expansion method, the Exp-function method and the extended tanh method. The suggested equation is converted into ordinary differential equation of fractional order with the aid of a suitable composite transformation and then the methods are applied to construct the solutions. The methods successfully provide many new and more general closed form traveling wave solutions. The obtained solutions may be more effective to analyze the nonlinear physical phenomena relevance to science and engineering than the existing results in literature. The performance of the proposed method is highly noticeable and this method will be used in further works to establish more entirely new solutions for other kinds of nonlinear fractional PDEs.

Keywords:

The fractional generalized (D G/G)-expansion method, the expfunction method,the extended tanh method,nonlinear fractional PDEs,conformable fractional derivative, composite transformation,closed form solutions,

Refference:

I.Alam, M. N. and Akbar, M. A. “The new approach of the generalized )/(GG-expansion method for nonlinear evolution equations”. Ain Shams Eng. J., Vol. 5 PP 595-603 (2014)

II.Alzaidy, J. F. “The fractional sub-equation method and exact analytical solutions for some fractional PDEs”. Amer. J. Math. Anal., PP 14-19 (2013)

III.Baleanu, D. Diethelm, K. Scalas, E. and Trujillo, J. J. “Fractional Calculus: Models and Numerical Methods”. Series on Complexity, Nonlinearity and Chaos, World Scientific Publishing, Boston, Mass, USA, Vol. 3 (2012)

IV.Deng, W. “Finite element method for the space and time fractional Fokker-Planck equation”. SIAM J. Numer. Anal., Vol. 47, PP 204-226 (2008)

V.Diethelm, K. “The analysis of fractional differential equations”. Springer-Verlag, Berlin, (2010)

VI.El-Sayed, A. M. A. and Gaber, M. “The Adomian decomposition method for solving partial differential equations of fractal order in finite domains”. Phys. Lett. A, Vol. 359, PP 175-182 (2006)

VII.El-Sayed, A. M. A., Behiry, S. H. and Raslan, W. E. “Adomian’s decomposition method for solving an intermediate fractional advection-dispersion equation”. Comput. Math. Appl., Vol. 59, PP 1759–1765 (2010)

VIII.Feng, J., Li, W. and Wan, Q. “Using )/(GG-expansion method to seek traveling wave solution of Kadomtsev-Petviashvili-Piskkunov equation”. Appl. Math. Comput., Vol. 217, PP 5860-5865 (2011)

IX.Gao, G. H., Sun, Z. Z. and Zhang, Y. N. “A finite difference scheme for fractional sub-diffusion equations on an unbounded domain using artificial boundary conditions”. J. Comput. Phys.,Vol. 231, PP 2865-2879 (2012)

X.Gepreel, K. A. “The homotopy perturbation method applied to nonlinear fractional Kadomtsev-Petviashvili-Piskkunov equations”. Appl. Math. Lett., Vol. 24, PP 1458-1434 (2011)

XI.Gepreel, K. A. and Omran, S. “Exact solutions for nonlinear partial fractional differential equations”. Chin. Phys. B, Vol. 21, PP 110204-110207 (2012)

XII.Guo, S., Mei, L., Li, Y. and Sun, Y. “The improved fractional sub-equation method and its applications to the space-time fractional differential equations in fluid mechanics”. Phys. Lett. A, Vol. 376, PP 407-411 (2012)

XIII.Hilfer, R. “Applications of Fractional Calculus in Physics”.World Scientific Publishing, River Edge, NJ, USA, (2000)

XIV.Hu, Y., Luo, Y. and Lu, Z. “Analytical solution of the linear fractional differential equation by Adomiandecomposition method”. J. Comput. Appl. Math., Vol. 215, PP 220-229 (2008)

XV.Huang, Q., Huang, G. and Zhan, H. “A finite element solution for the fractional advection-dispersion equation”. Adv. Water Resour., Vol. 31, 1578-1589 (2008)

XVI.Inc, M. “The approximate and exact solutions of the space-and time-fractional Burgers equations with initial conditions by variational iteration method”. J. Math. Anal. and Appl.Vol. 345, PP 476-484 (2008)

XVII.Islam, M. T., Akbar, M. A. and Azad, A. K. “A Rational )/(GG-expansion method and its application to the modified KdV-Burgers equation and the (2+1)-dimensional Boussinesq equation”. Nonlinear Studies, Vol. 6, PP 1-11 (2015)

XVIII.Khalil, R., Horani, M. A., Yousef, A. and Sababheh, M. “A new definition of fractional derivative”. J. Comput. Appl. Math., Vol. 264, PP 65-67 (2014)

XIX.Kilbas, A. A., Srivastava, H. M. and Trujillo, J. J. “Theory and Applications of Fractional Differential Equations”.North-Holland Mathematics Studies, Elsevier Science, Amsterdam, The Netherlands, Vol. 204 (2006)

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XXI.Li, C., Chen, A. and Ye, J. “Numerical approaches to fractional calculus and fractional ordinary differential equation”. J. Comput. Phys.,Vol. 230, PP 3352-3368 (2011)

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XXIV.Momani, S., Odibat, Z. and Erturk, V. S. “Generalized differential transform method for solving a space-and time-fractional diffusion-wave equation”. Phys. Lett. A, Vol. 370, PP 379-387 (2007)

XXV.Odibat, Z. and Momani, S. “A generalized differential transform method for linear partial differential equations of fractional order”. Appl. Math. Lett.,Vol. 21, PP 194-199 (2008)

XXVI.Odibat, Z. and Momani, S. “Fractional Green functions for linear time fractional equations of fractional order”. Appl. Math. Lett., Vol. 21, PP 194-199 (2008)

XXVII.Odibat, Z. and Momani, S. “The variational iteration method: an efficient scheme for handling fractional partial differential equations in fluid mechanics”. Comput. Math. Appl., 58, PP 2199–2208 (2009)

XXVIII.Oldham, K. B. and Spanier, J. “The Fractional Calculus”.Academic Press, New York, NY, USA, (1974)

XXIX.Podlubny, I. “Fractional Differential Equations”.Mathematics in Science and Engineering, Academic Press, San Diego, Calif, USA, Vol. 198 (1999)

XXX.Sabatier, J., Agrawal, O. P. and Machado, J. A. T. “Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering”.Springer, New York, NY, USA, (2007)

XXXI.Samko, S. G., Kilbas, A. A. and Marichev, O. I. “Fractional Integrals and Derivatives”.Gordon and Breach Science, Yverdon, Switzerland, (1993)

XXXII.West, B. J., Bologna, M. and Grigolini, P. “Physicsof Fractal Operators”.Springer, New York, NY, USA, (2003)

XXXIII.Wu, G. C. and Lee, E. W. M. “Fractional variational iteration method and its application”. Phys. Let. A, Vol. 374, PP 2506-2509 (2010 )

XXXIV.Yang, X. J. “Local Fractional Functional Analysis and Its Applications”.Asian Academic Publisher, Hong Kong, (2011)

XXXV.Yang, X. J. “Advanced Local Fractional Calculus and Its Applications”.World Science Publisher, New York NY, USA, (2012)

XXXVI.Zhang S. and Zhang, H. Q. “Fractional sub-equation method and itsapplications to nonlinear fractional PDEs”. Phys. Lett. A, Vol. 375, PP1069-1073 (2011)

XXXVII.Zhang, Y. and Feng, Q. “Fractional Riccati equation rational expansionmethod for fractional differential equations”.Appl. Math. Inf. Sci., Vol.PP 1575-1584 (2013)

XXXVIII Zheng, B. “)/(GG-expansion method for solving fractional partialdifferentialequations in the theory of mathematical physics”. Commu.Theore. Phys., Vol. 58, PP 623-630 (2012)

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Abstract:

In cooperative transmission selection of relay is considered to be the crucial factor for reliable transmission where multiple parameters are there for decision making. Again, many existing research works highlighted the problem, but none of them considered the vagueness & uncertainty of the decision makers. Currently, Fuzzy analytic hierarchy process (FAHP) proves to be an advantageous scheme for multiple criteria decision-making (MCDM) in fuzzy conditions. This paper provides FAHP-based relay node selection scheme that prioritizes the fuzziness of the decision makers during the relay node selection procedure. Numerical examples and simulation study, both are carried out to find out the best relay. The simulation study reveals the fact that the proposed scheme outperforms the existing systems.

Keywords:

Best Relay selection,Relay node,Cognitive radio Networks,Decision making,analytical hierarchy process,Fuzzy analytical hierarchy process,

Refference:

I.Akyildiz, I. F.; Wang, X. and Wang, W. “Wireless mesh networks: a survey”. Computer networks, 47(4), pp 445-487 (2005).

II.Akyildiz, I. F.; et. al. “CRAHNs: Cognitive radio ad hoc networks”. Ad Hoc Networks, 7(5), pp 810-836 (2009).

III.Buckley J. J. “Fuzzy hierarchical analysis. Fuzzy sets and systems”, 17(3), pp 233-247, (1985)

IV.Banerjee J.S.; Chakraborty A. and Chattopadhyay A. “Fuzzy Based RelaySelection for Secondary Transmission in Cooperative Cognitive RadioNetworks”. In: Proc. OPTRONIX, Springer, pp 279-287 (2017).

V.Banerjee J.S.; Chakraborty A and Chattopadhyay A. “Relay node selection using analytical hierarchy process (AHP) for secondary transmission in multi-user cooperative cognitive radio systems”. In: Proc. ETAEERE, Springer, pp 745-754 (2018).

VI.Banerjee, J. S. and Chakraborty, A. “Fundamentals of Software DefinedRadio and Cooperative Spectrum Sensing: A Step Ahead of CognitiveRadio Networks”. In Handbook of Research on Software-Defined andCognitive Radio Technologies for Dynamic Spectrum Management, IGIGlobal, pp 499-543 (2015).

VII.Banerjee, J.S.; Chakraborty, A. and Karmakar, K. “Architecture ofCognitive Radio Networks”. In N. Meghanathan & Y.B.Reddy (Ed.),Cognitive Radio Technology Applications for Wireless and Mobile AdHoc Networks, IGI Global, pp 125-152 (2013).

VIII.Banerjee, J.S. and Chakraborty, A. “Modeling of Software Defined RadioArchitecture & Cognitive Radio, the Next Generation Dynamic and SmartSpectrum Access Technology”. In M.H. Rehmani & Y. Faheem (Ed.),

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Abstract:

This paper deals withsteady two dimensional laminar convection flow of nano fluid over aconvective heated inclined plate.Boungiorno model [VI] is employed that treats the nanofluid as a two-component mixture (base fluid plus nanoparticles), incorporating the effects of Brownian motion and thermophoresis.Byappropriate similarvariables, the governing nonlinear partial differential equations of flow are transformed to a set of nonlinear ordinary differential equations. Subsequently they are reduced to a first order system and integrated using Newton Raphson and adaptive Runge-Kutta methods. The computer codes are developed for this numerical analysis in Matlab environment. Dimensionless stream function (s), longitudinal velocity (s′), temperature (θ) and nano particle volume fraction (f) are computed and illustrated graphically for various values of thedimensionless parameters relevant to the present problem. The effects of the angle of inclination on longitudinal velocity (s′), temperature (θ) and nano particle volume fraction (f) are discussed. The results of the present simulation are in with good agreement with the previous reports available in literature.

Keywords:

Brownian Motion,Boundary Layer,Convective Boundary Condition,Inclined Plate, Nano fluid,Thermophoresis,

Refference:

I. Alam,M., Rahman,M., Sattar,M.: On the effectiveness of viscous dissipation and joule heating on steady magnetohydrodynamic heat and mass transfer flow over an inclined radiate isothermal permeable surfacein the presence of thermophoresis. Commun.Nonlinear Sci. Numer.Simul.14, 2132–2143 (2009)

II. Anghel, M., Hossain, M.A., Zeb, S., Pop, I., Combined heat and mass transfer by free convection past aninclined flat plate. Int. J. Appl. Mech. Eng. 2, 473–497 (2001).

III. Ishak A., Similarity solutions for flow and heat transfer over a permeable surface with convective boundary condition, Appl. Math. Computation, 217(2010), 837-842. (periodical)

IV. Aziz A., A similarity Solution for Laminar Thermal Boundary Layer over a Flat Plate with a Convective Surface Boundary Condition, Commun. Nonlinear Sci. Numer.Simulat., 14 (2009), 1064-1068.

V.Bianchi M. V. A. and ViskantaR., Momentum and heat transfer on a continuous flat surface movingin a parallel counterflow free stream, W/irme-und Stoff/ibertragung 29, 89-94 (1993)

VI. Buongiorno J., Convective transport in nanofluids, ASME J. Heat Transf. 128 (2006) 240–250.

VII. Choi S., Enhancing thermal conductivity of fluids with nanoparticle in: D.A. Siginer, H.P. Wang (Eds.), Developments and Applications of Non-Newtonian Flows, ASME MD vol. 231 and FED vol. 66, 1995, pp. 99–105.

VIII. Chen, C.H., Heat andmass transfer inMHDflowby natural convection from a permeable, inclined surfacewith variable wall temperature and concentration. Acta Mech. 172, 219–235 (2004)

IX. Khan W. A. and Aziz A., Natural convection flow of a nanofluid over a vertical plate with uniform surface heat flux, International Journal of Thermal Sciences, 50 (2011) 1207-1214.

X. KuznetsovA.V. and NieldD.A., Natural convective boundary-layer flow of a nanofluid past a vertical plate, Int. J. Thermal Sciences, 49, (2010) 243–247.

XI. Makinde O. D. and Aziz A., Boundary Layer Flow of a Nanofluid Past a Stretching Sheet with Convective Boundary Condition, Int. J. Therm. Sci., 50 (2011), 1326-1332. (periodical)

XII. Mitra A., Computational Modeling of Boundary-Layer Flow of a Nanofluid Past a Nonlinearly Stretching Sheet ,J. Mech.Cont. & Math. Sci., Vol.-13, No.-1, March –April (2018) Pages 101-114.

XIII. NieldD.A. andKuznetsovA.V., Thermal instability in a porous medium layer saturated by a nanofluid, Int.J.Heat Mass Transf, 52 (2009) 5796–5801.

XIV. SuneethaS. and Gangadhar K., Thermal Radiation Effect on MHD Stagnation Point Flow of a Carreau Fluid with Convective Boundary Condition, Open Science Journal of Mathematics and Application, 3(5): 121-127, 2015.

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Abstract:

In the recent time,the research and development have been blooming in the field of the prosthetic system,especially on the prosthetic arm.Thispaper emphasizesa precise study of continues advancement of the prosthetic arm. The latest expansions of the prosthetic arm are renovated with implementations of biomedical innovations. Different novel approaches are reflected in a sort of research works with technical progress considering the diverse aspect of complexity, cost, size, material, dexterity, the degree of freedom. A Systematic research and development work on the prosthetic arm and Electromyography(EMG) controlled prosthetic arm devices, Electroneurographysignal (ENG) driven prosthetic arm and devices are deeply specified in this paper. The innate efforts of the scientists and researchers of this field as well as accumulated erudition from various research papers, books and patents areenlightened and assisted in this attempt of drawing a complete overview of arm prosthesis.

Keywords:

Prosthetic Arm,Bio-signal,Electromyography (EMG),Electroneurography (ENG), Electro-Mechanical Arm,

Refference:

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Abstract:

n this paper, we implement divide by 32/33 dual modulus prescaler(DMP) using I-ETSPC based: divide by 2/3prescaler and divide by 4/5 by prescaler at 180nm CMOS technology. The divide by 32/33 dual modulus prescaler using 2/3 prescaler and 4/5 prescaler consumes 1.03mW and 0.85mW power from 1.2V and 1V respectively. To further improve speed and reduce design complexity with low power consumption a pseudo divide by 32/33 dual modulus prescaler is proposed. According to simulation results the pseudo divide by 32/33 dual modulus prescaler reaches a maximum 9.2 GHz working frequency at 1V with a 0.17mw power consumption. This prescaler is compared with Proposed I-ETSPC based divide by 32/33 using 2/3 and 4/5 prescalers and also with other recently published divide by 32/33 prescalers.Compared with previous conventional divide by 32/33 DMPs, this design contains fewer transistor numbers.

Keywords:

2/3 prescaler, 4/5 prescaler, divide by 32/33 prescalers, I –ETSPC,Sleepy Keeper Approach,

Refference:

I.C. Lee, L. C. Cho and S. I. Liu, “A 44GHz Dual-Modulus Divide-by-4/5 Prescaler in 90nm CMOS Technology,” IEEE Custom Integrated Circuits Conference (CICC ’06),San Jose, CA, pp. 397-400, 2006.

II.F. P. H. Miranda, J. Navarro and W. A. M. Van Noije, “ A 4 GHz Dual Modulus Divider-by 32/33 Prescaler in 0.35μm CMOS Technology” In Proc. of the 17th annual symposium on Integrated circuits and system design(SBCCI‟04), Pernanbuco, Brazil, pp. 94-99, Sept. 7-11, 2004.

III.F. P. H. Miranda, J. Navarro and W. A. M. Van Noije,“A 4.1 GHz Prescaler Using Double Data Throughput E-TSPC Structures,” In Proc. of the 20th annual symposium on Integrated circuits and system design(SBCCI‟07),Rio de Janeiro, Brazil, pp. 123-127, Sept. 3-6, 2007.

IV.J. N. Soares, Jr. and W. A. M. Van Noije, “A 1.6-GHz dual modulus prescaler using the extended true-single-phase-clock CMOS circuit technique (E-TSPC),” IEEE J. Solid-State Circuits, vol. 34, no. 1, pp. 97–102, Jan. 1999.

V.J.C. Park, V. J. Mooney, P. Pfeiffenberger, “Sleepy Stack Reduction of Leakage Power”,Proceeding of the International Workshop on Power and Timing Modeling Optimization and Simulation, pp. 148-158, September 2004.

VI.J. Wu, et al.: “A low-power high-speed true single phase clock divide-by-2/3 prescaler,” IEICE Electron. Express10 (2013) 20120913 (DOI: 10.1587/elex. 10.20120913).

VII.J. Navarro, and G. C. Martins, “Design of High Speed Digital Circuits with E-TSPC Cell Library,” In Proc. of the 24th symposium on Integrated circuits and systems design(SBCCI ’11), João Pessoa, Brazil, pp. 167-172, Aug. 30–Sept. 2, 2011 .

VIII.M. V. Krishna, M. A. Do, K. S. Yeo, C. C. Boon, and W. M. Lim, “Design and analysis of ultra-low power true single phase clock CMOS2/3 prescaler,” IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 57, no. 1, pp. 72–82, Jan. 2010.

IX.R Jain, U Nirmal et al “Design and Optimization of Pseudo-NMOS basedImproved extended True Single-Phase Clock Technique low-Power Prescaler”, International Conference on Soft Computing,Intelligent Systems and Applications, April 8-9, 2016, Bangalore, India.

X.R. Jain, U. Nirmal et al., “Low Voltage Low Power 4/5 Dual Modulus Prescaler in 180nm CMOS Technology”, International Conference on Research Advances in Integrated Navigation Systems(RAINS -2016), May 6-7, 2016.

XI.S. Bhargava, U. Nirmal, “AUnified Approach in the Analysis of Prescalers and Dual Modulus Prescalers for low-power systems”International Journal of Applied Engineering Research ISSN 0973-4562 Volume 12, Number 12 (2017) pp. 3042-3048.

XII.S. Pellerano , S. Levantino , C. Samori , and A. L. Lacaita, “ A 13.5-mW 5-GHz Frequency Synthesizer with dynamic-logic frequency divider,” IEEE J. Solid-State Circuits, vol. 39, no. 2, pp. 378–383, Feb. 2004.

XIII.Song Jia, Shilin Yan et al, “Low-power, high-speed dual modulus prescaler based on branch-merged true single-phase clocked scheme” ELECTRONICS LETTERS,Vol. 51 No. 6 pp. 464–465, March 2015.

XIV.W.-H. Chen and B. Jung, “High-speed low-power true single-phase clock dual-modulus prescalers,” IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 58, no. 3, pp. 144 –148, March 2011.

XV.W Jiang et. Al., “A low-power high-speed true single-phase clock-based divide-by-2/3 prescaler” IEICE Electronics Express, Vol 14, No. 1, 1 –6, 2017.

XVI.Xincun Ji et. Al., “ A 2.4 GHz fractional-N PLL with a low power true single phase clock prescaler ” IEICE Electronics Express, Vol 14, No. 8, 1 –8, 2017.

XVII.X.P. Yu, M.A. Do, W. M. Lim, K. S. Yeo, and J. G. Ma, “Design and optimization of the extended true single-phase clock-based prescaler,” IEEE Trans. Microwave Theory Tech., vol. 54, no. 11, pp. 3828–3835, Nov. 2006.

XVIII.Z. Deng and A. Niknejad, “The speed-power trade-off in the design of CMOS true-single-phase-clock dividers,” IEEE Journal of Solid-State Circuits, vol. 45, no. 11, pp. 2457 –2465, Nov. 2010.

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Abstract:

Observing the effect of PSO algorithm on the PID (Proportional-Integral-Derivative) controller is an advanced approach for getting a stable and linear response of any system. From few decades conventional PID tuning rules are used for analyzing any complex system. But these rules did not give always a satisfactory result as our requirement. That’s why a better algorithm was introduced which is actually based on Evolutionary Computation method. This methodology provides a very high accuracy in the response in comparison with other tuning rules.From thevery past, PID controller has been very popular and is being used in maximum industries. So, there’s always a need to control the accuracy and efficiency of the controller because depending on this controller the whole industry might be functioning. If any large error occurs in the controller (PID), the functioning of the industry might be hampered. That’s why using PSO algorithm for determining the PID parameter is a good idea to get an efficient and accurate output. This approach may help in future to improve the performance of PID controller and also may help to reduce errors encountered in the industries.

Keywords:

Particle Swarm Optimization (PSO),Evolutionary Computation Method,PID (Proportional-Integral-Derivative) controller,Ziegler-Nichols tuning method,

Refference:

I.Ankita Nayak, Mahesh Singh. “Study of Tuning of PID controllers by using Particle Swarm Optimization”. Int. J. Adv. Engg. Res. Studies/IV/II/Jan.-March,2015/346-350.

II.Arnob Senapati, A. K. Kashyap, B. K. Mondal, S. Chattarjee. “Speed performance Analysis of DC Servomotor Using Linear and Non Linear Controller”.International Journal for Research in Applied Science & Engineering Technology, Volume 6 Issue III, March 2018.

III.K.Lakshmi Sowjanya, L.Ravi Srinivas. “Tuning of PID controllers using Particle Swarm Optimization”. IJIEEE, Volume-3, Issue-2, Feb-2015.

IV.Mahmud Iwan Solihin, Lee Fook Tack, Moey Leap Kean. “Tuning of PID controllers using Particle Swarm Optimization”. ISC 2011, Malaysia, 14-15 January 2011.

V.Neha Kundariya, Jyoti Ohri. “Tuning of PID Controller for Time Delayed Process using Particle Swarm Optimization”. IJSET, Volume No.2, Issue No.7, PP: 665-669.

VI.S. Easter Selvan, Sethu Subramanian, S. Theban Solomon. “Novel Technique for PID Tuning by Particle Swarm Optimization”.

VII.S.M.GirirajKumar, Deepak Jayaraj, Anoop.R.Kishan. “PSO based Tuning of a PID Controller for a High Performance Drilling Machine”. International Journal of Computer Applications (0975-8887), Volume 1-No. 19.

VIII.Subhojit Malik, Palash Dutta, Sayantan Chakrabarti, Abhishek Barman. “Parameter Estimation of a PID Controller using Particle Swarm Optimization”. IJARCCE, Vol. 3, Issue 3, March 2014.

IX.Turki Y. Abdalla, Abdulkareem. A. A. “PSO-based Optimum design of PID Controller for Mobile Roboat Trajectory Tracking”. International Journal of Computer Applications (0975-8887), Volume 47-No. 23, June 2012.

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