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Nonexistence of periodic solutions and asymptotically periodic solutions for fractional differential equations. (English) Zbl 1253.35204

Summary: Using the final value theorem of Laplace transform, it is firstly shown that nonhomogeneous fractional Cauchy problem does not have nonzero periodic solution. Secondly, two basic existence and uniqueness results for asymptotically periodic solution of semilinear fractional Cauchy problem in an asymptotically periodic functions space. Furthermore, existence and uniqueness results are extended to a closed, nonempty and convex set which is a subset of a Fréchet space. Some examples are given to illustrate the results.

MSC:

35R11 Fractional partial differential equations
35B10 Periodic solutions to PDEs
35B40 Asymptotic behavior of solutions to PDEs
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