Generalized fractional integration of k\-Bessel function

TL;DR

This paper introduces generalized fractional integral transforms involving the k-Bessel function and hypergeometric functions, providing composition formulas and relations to classical fractional integrals.

Contribution

It develops new composition formulas for generalized fractional integrals with k-Bessel functions using hypergeometric functions, extending classical fractional calculus.

Findings

Derived composition formulas for generalized fractional integrals with k-Bessel functions.

Established relations between these generalized integrals and classical Riemann-Liouville and Erdélyi-Kober transforms.

Expressed results in terms of Wright type hypergeometric functions.

Abstract

In this present paper our aim is to deal with two integral transforms which involving the Gauss hypergeometric function as its kernels. We prove some compositions formulas for such a generalized fractional integrals with k Bessel function. The results are established in terms of generalized Wright type hypergeometric function and generalized hypergeometric series. Also, the authors presented some corresponding assertions for Riemann Liouville and Erdelyi Kober fractional integral transforms.