Solution of fractional kinetic equations involving class of functions and Sumudu transform

Kottakkaran Sooppy Nisar,Gauhar Rahman,Dinesh Kumar,Amjad Shaikh

doi:10.1186/s13662-020-2513-6

Abstract

Fractional kinetic equations (FKEs) including a wide variety of special functions have been widely and successfully applied in describing and solving many important problems of physics and astrophysics. In this paper, we derive the solutions for FKEs including the class of functions with the help of Sumudu transforms. Many important special cases are then revealed and analyzed. The use of the class of functions to obtain the solution of FKEs is fairly general and can be efficiently used to construct several well-known and novel FKEs.

Highlights

Fractional calculus has been developed and used in different fields of applied science and engineering
From Theorem 2.2 and Theorem 2.3, one can deduce many known and new solutions of the fractional kinetic equation involving a variety of special functions
The graphical results demonstrate that the region of convergence of solutions depends continuously on the fractional parameter ν as well as on λ

Summary

Introduction

1 Introduction Fractional calculus has been developed and used in different fields of applied science and engineering. The fractional generalized form of the standard kinetic equation (1.3) is given in [15] as Another generalized form of FKE is given in [36] as

Objectives

Results

Conclusion