Nonexistence of periodic solutions and asymptotically periodic solutions for fractional differential equations |
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| Authors: | JinRong Wang Michal Fec˘kan Yong Zhou |
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| Affiliation: | 1. Department of Mathematics, Guizhou University, Guiyang, Guizhou 550025, PR China;2. Department of Mathematical Analysis and Numerical Mathematics, Faculty of Mathematics, Physics and Informatics, Comenius University, Mlynskádolina, 842 48 Bratislava, Slovakia;3. Mathematical Institute, Slovak Academy of Sciences, ?tefánikova 49, 814 73 Bratislava, Slovakia;4. Department of Mathematics, Xiangtan University, Xiangtan, Hunan 411105, PR China |
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| Abstract: | 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. |
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