Weighted pseudo almost automorphic mild solutions to semilinear fractional differential equations

Abstract

This paper is concerned with the existence and uniqueness of weighted pseudo almost automorphic mild solution to the semilinear fractional equation: D t α u ( t ) = Au ( t ) + D t α - 1 f ( t , u ( t ) , Bu ( t ) ) , t ∈ R , 1 < α < 2 where A is a linear densely defined operator of sectorial type on a complex Banach space X and B is a bounded linear operator defined on X . Under the assumption of uniformly continuity on f, we establish a composition of weighted pseudo almost automorphic in a general Banach space and obtain existence results by means of Banach contraction mapping. The results obtained are utilized to study the existence and uniqueness of a weighted pseudo almost automorphic solution to fractional diffusion wave equation with Dirichlet conditions.