Existence of almost periodic solution for nonlocal fractional Cauchy problem with integral initial condition

Abstract

In this research, we intend to show that the nonlocal fractional Cauchy problem Dαu(t)=A(t)u(t)+f(t,u(t)), t∈J=[0,1] with integral initial condition u(0)=∫01g(s,u(s))ds, in the Banach space X, where A is a generator of α-resolvent operator function {T(t)}t≥0 and f, g are given functions satisfying some assumptions, has an almost periodic solution.