In this paper, we prove that Caputo type linear fractional evolution equations do not have nonconstant periodic solutions. Then, we study asymptotically periodic solutions of semilinear fractional evolution equations and establish existence and uniqueness results by using theory of semigroup and fixed point theorems. Finally, two examples are given to illustrate the theoretical results.

In this paper we investigate the asymptotically periodic behavior of solutions of fractional evolution equations of order 1 < α < 2 and in particular existence and uniqueness results are established. Two examples are given to illustrate our results.

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In this paper, we study a class of (ω, c)-periodic time varying impulsive differential equations and establish the existence and uniqueness results for (ω, c)-periodic solutions of homogeneous problem as well as nonhomogeneous problem.

In this paper, existence and uniqueness of periodic solutions of second‐order semilinear impulsive differential equations are obtained. Some sufficient conditions that guarantee the existence of periodic solutions to second‐order linear nonhomogeneous impulsive differential equations are obtained. In addition, by using the appropriate fixed theorem and the theory of coincidence degree, some conditions ensuring the existence and uniqueness of periodic solution to second‐order semilinear impulsive differential systems are derived. Finally, some examples are provided to illustrate the availability of our results.