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Note on Periodic and Asymptotically Periodic Solutions of Fractional Differential Equations

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Applied Mathematical Analysis: Theory, Methods, and Applications

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 177))

Abstract

Several results are presented on the existence or nonexistence of periodic solutions for fractional differential equations (FDEs for short) on arbitrary dimensional spaces involving Caputo fractional derivatives. The existence of S-asymptotically periodic solutions as well as periodic boundary value problems are also investigated. A rather broad variety of FDEs is considered by covering both finite dimensional FDEs and evolution FDEs in infinite dimensional spaces containing either single order or mixed orders of Caputo fractional derivatives with either finite or infinite lower limits of Caputo fractional derivatives. Different qualitative results are derived for particular types of studied FDEs, for instance, a uniform upper bound for Lyapunov exponents of solutions. Several examples are presented to illustrate theoretical results, such as fractional Duffing equations or periodically forced nonlinear fractional wave equations.

This work was supported by the Slovak Research and Development Agency (grant number APVV- 14-0378) and the Slovak Grant Agency VEGA (grant numbers 2/0153/16 and 1/0078/17).

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Authors and Affiliations

  1. Department of Mathematical Analysis and Numerical Mathematics, Faculty of Mathematics, Physics and Informatics, Comenius University in Bratislava, Mlynská dolina, 842 48, Bratislava, Slovakia

    Michal Fečkan

  2. Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, 814 73, Bratislava, Slovakia

    Michal Fečkan

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  1. Michal Fečkan
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Correspondence to Michal Fečkan .

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Editors and Affiliations

  1. Department of Mathematics, Gauhati University, Guwahati, India

    Hemen Dutta

  2. Computational Intelligence Laboratory, Department of Electrical & Computer Engineering, University of Manitoba, Winnipeg, MB, Canada

    James F. Peters

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Fečkan, M. (2020). Note on Periodic and Asymptotically Periodic Solutions of Fractional Differential Equations. In: Dutta, H., Peters, J. (eds) Applied Mathematical Analysis: Theory, Methods, and Applications. Studies in Systems, Decision and Control, vol 177. Springer, Cham. https://doi.org/10.1007/978-3-319-99918-0_6

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