Some sufficient conditions on impulsive and initial value fractional order functional differential equations

TL;DR

This paper establishes conditions for the existence and uniqueness of mild solutions to impulsive fractional differential equations with initial value and state-dependent delay, using fixed point theorems and an example.

Contribution

It introduces a new definition of mild solutions for impulsive fractional differential equations of order between 1 and 2, and proves existence and uniqueness results.

Findings

Existence of mild solutions under certain conditions.

Uniqueness of solutions demonstrated.

Application to a partial fractional derivative example.

Abstract

In this paper, we will develop a definition of mild solution for impulsive fractional differential equation of order $\alpha\in (1,2)$ with the help of solution operator and study the existence results of mild solution for impulsive fractional differential equations with state dependent delay by using fixed point theorems. Finally, we present an example of partial fractional derivative to illustrate the existence and uniqueness result.