Nonexistence of periodic solutions and asymptotically periodic solutions for fractional differential equations

摘要

Using the final value theorem of Laplace transform, it is firstly shown that nonhomogene-ous 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 Frechet space. Some examples are given to illustrate the results.