Asymptotically automorphic solutions of abstract fractional evolution equations with non-instantaneous impulses

Abstract

In this paper, we study the existence of asymptotically automorphic mild solutions of fractional evolution equations with non-instantaneous impulses. The main results are based upon some properties of sectorial operators, and Krasnoselkii fixed point theorem. A new set of sufficient conditions is formulated which guarantees the existence of the solution of the non-instantaneous system. An example is also discussed to illustrate the efficiency of the obtained results.

Keywords

• asymptotically almost automorphic
• abstract fractional equations
• sectorial operator
• fixed point theorem
• non-instantaneous impulses