Authors:
Dilip Kumar Jaiswal,Surekha Dewangan,D. S. Singh,DOI NO:
https://doi.org/10.26782/jmcms.2024.10.00010Keywords:
ARA transform,Laplace transform,Triple Laplace-ARA transform,Volterra Integral equation,Volterra-integrodifferential equation,integro-partial differential equation,Abstract
To solve differential equations, we utilize an extended Laplace-ARA transform result that we offer in this work to verify the existence of other pertinent theorems.Refference:
I. AL-Qmari S. K. Q. (2020), Estimation of a modified integral associated with a special function kernel of fox’s h-function type, Commun. Korean Math. Soc. , No. 1, pp. 125–136.
II. BhatterSanjay(2022), On Certain New Results of Fractional Calculus Involving Product of Generalized Special Functions, Int. J. Appl. Comput. Math. 10.1007/s40819-022-01253-0.
III. Choi J. H.(2013), Applications of multivalent functions associated with generalized fractional integral operator, Scientific Research, Advances in Pure Mathematics, 3, 1 – 5.
IV. Debnath, L., Bhatta, D.: Integral Transforms and Their Applications, 3rd edn. Chapman Haubold H. J.(2009), Mittag-Leffler Functions and their applications, Journal of Applied Mathematics, arXiv:0909.0230v2 .
V. Gupta K.(2011), A Study of modified H-transform and generalized fractional integral operator of weyl type, International Journal of Pure and Applied Sciences and Technology, 7(1) (2011), pp. 59-67, ISSN 2229-6107.
VI. Gupta K. and Vandana Agrawal (2010). A Theorem Connecting the H-Transform and Fractional Integral Operators Involving the Multivariable H-Function*, Tamsui Oxford Journal of Mathematical Sciences, Aletheia University, 26(4) , 383-395.
VII. Gupta K. C. and Gupta T. (2005), On unified Eulerian type integrals having general arguments, Soochow Journal of Mathematics, Volume – 31, No. 4, pp. 543-548.
VIII. Haubold H. J.(2009). Mittag-Leffler Functions and their applications, Journal of Applied Mathematics, arXiv:0909.0230v2 .
IX. Jangid K.(2020),Fractional calculus and integral transforms of the product of a general class of polynomial and incomplete Fox–Wright functions , Advances in Difference Equations , 2020:606 https://doi.org/10.1186/s13662-020-03067-0
X. Koul C. L(1971), On fractional integral operators of functions of two variables, Proc. Nat. Acad. Sci.India,41A,233-240.
XI. Kumar D (2013), Generalized Fractional Differentiation of the–Function Involving General Class of Polynomials, Int. J. Pure Appl. Sci. Technol., 16(2) , pp. 42-53, 2229 – 6107.
XII. Kumar D.(2013), New Fractional-Calculus Results Involving General Class of Multivariable Polynomials and Multivariable H-function, International Journal of Modern Mathematical Sciences. 7(1): 55-64,2166-286X.
XIII. Kiryakoya V.(2010),The special functions of fractional calculus as generalized fractional calculus operators of some basic functions, Comp& mathematics with applications, 59(3) ,1128-1141. 10.1016/j.camwa.2009.05.014.
XIV. Oparnica L (2001), Generalized fractional calculus with applications in mechanics, MATEMATИЧKИ BECHИK, 53, 151 – 158.
XV. Singh S.K. (2018), Integral Transform and the Solution of Fractional Kinetic Equation Involving Some Special Functions, International Journal of Mathematics Trends and Technology (/IJMTT) –V (55), pp. 5- 16.
XVI. Satyanarayana B. and Kumar Pragathi(2011). Some finite integrals involving multivariable polynomials, H-function of one variable and H-function of ‘r’ variables, African Journal of Mathematics and Computer Science Research Vol. 4(8), pp. 281-285.
XVII. Sharma B. L(1961), On a generalized function of two variables, I. Ann. Soc. Sci., Bruxellers Ser. I 79(1965), 26-40.Fox C. The G and H-functions as symmetrical Fourier kernel, Amer. Math. Soc. Transl., 98 , pp.395-429
XVIII. Srivastava H. M. (1983). The Weyl fractional integral of a general class of polynomials, Boll. Un. Mat. Italy 602-B , pp.219-228.
XIX. Srivastava H. M.(1976), Some bilateral generating functions for a class of generalized hypergeometric polynomials, J. Reine Angew. Math., 283/284, 265-274.
XX. Thakur A.K, S.K. Sahani and J.K. Kushwaha (2020), Some applications of Quadraple Hypergeometric functions in functions Spaces, Vol 17(12) 894 -903| 10.5281/zenodo.7451049.
View Download