This paper is concerned with the existence and uniqueness of weighted pseudo almost
automorphic mild solution to the semilinear fractional equation: Dtαu (t)= Au (t)+ Dtα-1f (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 …

This paper is concerned with the existence and uniqueness of a weighted pseudo almost
automorphic mild solution to the semilinear fractional equation: Dtαu (t)= Au (t)+ Dtα− 1f (t, u
(t)), t∈ R, 1< α< 2 in complex Banach spaces with Sp-weighted pseudo almost automorphic
coefficients, where A is a linear densely defined operator of sectorial type on a complex
Banach space X. Moreover, we present an application to a fractional wave equation.