Weighted pseudo almost automorphic functions with applications to impulsive fractional integro-differential equation

Abstract

This paper’s main motivation is to study the notion of weighted pseudo almost automorphic (𝒲𝒫𝒜𝒜) functions and establish the existence results of piecewise continuous mild solution of fractional order integro-differential equation with instantaneous impulses. The usual 𝒲𝒫𝒜𝒜 functions may not work since the solution of impulsive differential equations may not be continuous. Thus in order to give a broader spectrum, we introduce this concept. We establish main results by using the Banach contraction mapping principle and Sadovskii’s fixed point theorem. An example is shown to exhibit our analytic findings.

Keywords

• integro-differential equation
• fractional order differential equation
• impulsive conditions
• weighted pseudo almost automorphic function
• primary 26a33
• secondary 34a37, 47g20