Results of local and global mild solution for impulsive fractional differential equation with state dependent delay

Abstract

In this paper, we establish the existence of local and global mild solution for an impul- sive fractional integro-differential equation with state dependent delay subject to nonlocal initial condition. The existence results for local mild solution are proved by applying the Schauder, nonlinear Larey Schauder alternative and Banach fixed point theorems. Then, we prove global existence result. An example is presented to demonstrate the application of the established re- sults.