Certain Image Formulae and Fractional Kinetic Equations of Generalized $$\mathtt {k}$$-Bessel Functions via the Sumudu Transform

Kottakkaran Sooppy Nisar,Fethi Bin Muhammad Belgacem,Moheb Saad Abouzaid

doi:10.1007/s40819-020-00866-7

Abstract

The monotonicity and the representation formulae of generalized $$\mathtt {k}$$ -Bessel functions, $$W_{\nu ,c}^{\mathtt {k}}$$ , studied by SR Mondal. This paper establishes the image formulae and then extract the solutions for fractional kinetic equations, involving $$W_{\nu ,c}^{\mathtt {k}}$$ utilizing their Sumudu transforms. Some significant particular cases are then deduced and analyzed.

Highlights

Fractional calculus; k-bessel function; fractional kinetic equations; laplace transforms
The k-Bessel function of the first kind defined by the following series [30]: Jkη,ξδ (z)
SR Mondal [24] gives the new generalization of k-Bessel function Wkν,c and is defined by

Summary

Introduction

Fractional calculus; k-bessel function; fractional kinetic equations; laplace transforms. The generalized Wright hypergeometric function pψq(z) is given by the series [42] SR Mondal [24] gives the new generalization of k-Bessel function Wkν,c and is defined by The Sumudu transform over the set functions

Objectives

Results

Conclusion