Authors:
Ghulam Muhammad,Sadaqat Hussain,DOI NO:
https://doi.org/10.26782/jmcms.2022.09.00001Keywords:
Time scales,Anderson’s inequality,∇ - differentiable,Abstract
Basically, time scale calculus is the theory of unification of traditional calculus with that calculus of difference i.e. discrete calculus. Time Scale Calculus is a field of discussion in the area of traditional analysis of mathematics. It focuses on the dynamic system which has a lot of applications in various fields of life. Calculus of time scales is a valuable field due to numerous applications in covid-19 disease cases. Notably, Time scale calculus has a long relation with mathematical inequalities that can be discussed with fractional calculus. The Anderson Integral Inequality, which provides a lower constraint for the integration of convex mapping in the form of the averages of each constituent, is described in this research paper on ∇- time-scale calculus. On ∇-time scale we formulated Anderson’s integral inequality as given below: if φ_j (j=1,….,α) accomplish some appropriate cases.Refference:
I. A.M. Fink Anderson’s inequality, Math. Inequal. Appl. 6 (2003) 241-245.
II. B. Aulbach. S. Hilger, Linear dynamic processes with inhomogeneous time scales, in: Nonlinear Dynamics and Quantum Dynamical systems, Akademie Verlag, Berlin, 1990.
III. B. Kaymakcalan, V. Lakshmikantham, S. Sivasundaram, Dynamic Systems on Measure Chains, Kluwer academic Publishers, Dordrecht, 1996.
IV. B.Z. Anderson, An inequality for convex functions, Nordisk Mat. Tidsk 6
(1958) 25-26.
V. D.S. Mitrinovic, J.E. Pecaric, A.M. Fink, Classical and New inequalities in Analysis, Kluwer Academic Publisher, Dordrecht, Boston, London, 199.
VI. M Bohner, A. Peterson, Dynamic Equations on Time Scales, Birkhauser,
Boston, Basel, Berlin, 2001.
VII. S. Hilger, Analysis on measure chains –A unified approach to continuous and discrete calculus, Res Math. 18 (1990) 28-56.