Weighted pseudo almost automorphic solutions of fractional functional differential equations

Abstract

In this paper we discuss the existence of weighted pseudo almost automorphic solution of fractional order functional differential equations. Using the fixed point theorem we establish existence and uniqueness of solution to the problem under consideration. The results obtained extend the theory of almost automorphic solutions to a more general class of weighted pseudo almost automorphic solutions. These extensions allow to treat infinite dimensional dynamics such as fractional wave and heat equation which are presented in the paper. At the end we give several example to illustrate the analytical findings.