In this research, we intend to show that the nonlocal fractional Cauchy problem Dαu(t) = A(t)u(t) + f(t; u(t)), t 2 J = [0; 1] with integral initial condition u(0) = R01 g(s; u(s))ds, in the Banach space X, where A is a generator of α- resolvent operator function fT (t)gt≥0 and f, g are given functions satisfying some assumptions, has an almost periodic solution.
