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WEll-Posedness of General Caputo-Type Fractional Differential Equations

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Abstract

In the present paper, initial value problems of fractional differential equations are considered. The fractional derivatives are defined as the general Caputo-type fractional derivatives proposed by Anatoly Kochubei. By using the Schauder fixed point theorem, the local existence, the global existence and the uniqueness of solutions are obtained under appropriate conditions. In addition, it is proved that the solution depends on the parameters of the equation in a continuous way.

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Authors and Affiliations

  1. School of Economics and Management, University of Science and Technology Beijing, 30 Xueyuan Road, Haidian District, Beijing, China

    Chung-Sik Sin

  2. Faculty of Mathematics, Kim Il Sung University, Ryomyong Street, Taesong District, Pyongyang, Korea

    Chung-Sik Sin

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  1. Chung-Sik Sin
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Sin, CS. WEll-Posedness of General Caputo-Type Fractional Differential Equations. FCAA 21, 819–832 (2018). https://doi.org/10.1515/fca-2018-0043

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  • DOI: https://doi.org/10.1515/fca-2018-0043

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