# A generalized Gronwall Inequality for Caputo Fractional Dynamic delta operator

## TL;DR

This paper develops a generalized Gronwall inequality using the Caputo fractional delta operator and applies it to establish the existence and properties of solutions for fractional dynamic equations.

## Contribution

It introduces a new generalized Gronwall inequality for Caputo fractional delta operators and uses it to analyze solutions of fractional dynamic equations.

## Key findings

- Established a generalized Gronwall inequality for Caputo fractional delta operator.
- Proved existence of solutions for Cauchy's type fractional dynamic equations.
- Analyzed properties of solutions using the new inequality.

## Abstract

In this paper we obtain generalized Gronwall type inequality using Caputo Fractional delta operator. Also we have obtained the existence of solution of Cauchy's Type problem on fractional dynamic equations using dynamic delta operator. Applying the obtained inequality we study the properties of solution on fractional dynamic equations.