Marichev-Saigo-Maeda fractional integration operators of generalized Bessel functions

TL;DR

This paper investigates fractional integration operators involving generalized Bessel functions, expressing their compositions with special functions in terms of Wright and hypergeometric functions, and explores various special cases.

Contribution

It introduces new integral operators with Appell and Horn functions in the kernel and derives their expressions with generalized Bessel functions, including special cases like sine and cosine.

Findings

Expressions in terms of Wright functions and hypergeometric series

Derivation of special cases involving trigonometric functions

Extension of fractional integration operators to generalized Bessel functions

Abstract

Two integral operator involving the Appell's functions, or Horn's function in the kernel are considered. Composition of such functions with generalized Bessel functions of the first kind are expressed in term of generalized Wright function and generalized hypergeometric series. Many special cases, including cosine and sine function are also discussed.