# Study of new class of q-fractional integral operator

## TL;DR

This paper introduces a new class of q-fractional integral operators using an iterated Cauchy integral approach, generalizing existing q-analogues of fractional differential operators and exploring their properties.

## Contribution

It presents a novel q-fractional integral operator that extends previous operators and encompasses the q-analogue of Hadamard fractional differential operator.

## Key findings

- The new operator generalizes existing q-fractional operators.
- Properties of the new q-fractional integral operator are investigated.
- The operator covers the q-analogue of Hadamard fractional differential operator.

## Abstract

We study the new class of q-fractional integral operator. In the aid of iterated Cauchy integral approach to fractional integral operator, we applied t^pf(t) instead of f(t) in these integrals and with parameter p a new class of q-fractional integral operator is introduced. Recently the q-analogue of fractional differential integral operator is studied.[8][4][9][10][13][14]All of these operators are q-analogue of Riemann fractional differential operator. The new class of introduced operator generalize all these defined operator and can be cover the q-analogue of Hadamard fractional differential operator. Some properties of this operator is investigated.