Existence of S-Asymptotically !-Periodic Solutions for Two-times Fractional Order Differential Equations ∗

Using a generalization of the semigroup theory of linear operators, we prove existence and uniqueness of S-asymptotically !-periodic mild solutions for a class of linear and semilinear fractional order differential equations of the form D +1 t u(t) + D t u(t)−Au(t) = f(t, u(t)), t > 0, 0 < ≤ ≤ 1, ≥ 0.

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