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Periodic Problem for Two-Term Fractional Differential Equations

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Abstract

We discuss the existence, multiplicity and uniqueness of solutions to the periodic problem cDαu + q(t, u)cDβu = f(t, {vnu}), {vnu}(0) = u({vnT}), where 0 > β > α ≤ 1. The existence results are proved by the combination of the Schauder fixed point theorem with the maximum principle for the Caputo fractional derivative and the structure of compact sets in R.

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Authors and Affiliations

  1. Department of Mathematical Analysis, Faculty of Science Palacký University, 17. listopadu 12–, 771 46, Olomouc, Czech Republic

    Svatoslav Staněk

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  1. Svatoslav Staněk
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Correspondence to Svatoslav Staněk.

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Staněk, S. Periodic Problem for Two-Term Fractional Differential Equations. FCAA 20, 662–678 (2017). https://doi.org/10.1515/fca-2017-0035

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  • DOI: https://doi.org/10.1515/fca-2017-0035

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