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

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.