Impulsive fractional differential inclusions with state-dependent delay

Abstract

In this paper, we prove the existence of mild solution for impulsive fractional inclusions with state-dependent delay in Banach spaces. Our study is based on the nonlinear alternative of Leray-Schauder type for multivalued maps due to Martelli. An example is provided to illustrate the main result.

Keywords

• impulsive fractional differential inclusions
• a-resolvent family
• solution operator
• caputo fractional derivative
• mild solution
• multivalued map
• fixed point
• banach spaces