$(\mu_1, \mu_2)-$Pseudo almost automorphic solutions of fractional order neutral integro-differential equations

Abstract

In this manuscript, a class of fractional order neutral differential equation is studied. Based on the theory of fractional calculus and the resolvent operator, the existence of $(\mu_1, \mu_2)$-pseudo almost automorphic(in short PAA) solution is established. The composition theorem for such functions is established, which is an important result in the field of qualitative theory of differential equations. An example is also presented to validate the feasibility of the proposed results