# Study of new class of q-fractional derivative and its properties

## TL;DR

This paper introduces a new Caputo-type q-fractional derivative, explores its properties, and studies related q-difference equations, including existence and uniqueness results using q-approximation methods.

## Contribution

It presents a novel Caputo-type q-fractional derivative and analyzes its properties and applications to q-difference equations, expanding fractional calculus in q-calculus context.

## Key findings

- The new q-fractional derivative is bounded.
- Existence and uniqueness of solutions to related q-difference equations are established.
- Properties of the new operator are systematically investigated.

## Abstract

There are several approaches to the fractional differential operator. Generalized q-fractional difference operator was defined in the aid of q-iterated Cauchy integral and q-calculus techniques. We introduce Caputo type derivative related to this operator and some properties of this operator as boundness are investigated. Moreover, related q-difference equation is discussed and in the aid of q-successive approximation , existence and uniqueness are studied.