# Certain composition formulae for the fractional integral operators

## TL;DR

This paper derives new composition formulas for fractional integral operators, including an integral operator with a Fox's H-function kernel, expanding the analytical tools available for engineering and mathematical analysis.

## Contribution

It introduces new expressions for the composition of fractional integral operators and defines a novel integral operator involving Fox's H-function, generalizing existing formulas.

## Key findings

- Derived new composition formulas for fractional integrals.
- Introduced an integral operator with Fox's H-function kernel.
- Unified various known and new expressions as special cases.

## Abstract

In this paper we establish some (presumably new) interesting expressions for the composition of some well known fractional integral operators $ I^{\mu}_{a+}, D^{\mu}_{a+} $,$ I^{\gamma , \mu}_{a+}$ and also derive an integral operator $\mathcal{H}^{w;m,n;\alpha}_{a+;p,q;\beta}$ whose kernel involve the Fox's $H-$ function. By suitably specializing the coefficients and the parameters in these functions we can get a large number of (new and known) interesting expressions for the composition formulae which occur rather frequently in many problems of engineering and mathematical analysis but here we can mention only those which follow as particular cases of the Srivastava et al.\cite{ZT}.