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Existence results of fractional differential equations with Riesz–Caputo derivative

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Abstract

This paper is concerned with a class of boundary value problems for fractional differential equations with the Riesz–Caputo derivative, which holds two-sided nonlocal effects. By means of a new fractional Gronwall inequalities and some fixed point theorems, we obtained some existence results of solutions. Three examples are given to illustrate the results.

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Authors and Affiliations

  1. College of Mathematics and Finance, Xiangnan University, Chenzhou, 423000, P.R. China

    Fulai Chen

  2. Department of Mathematics and Computer Sciences, Cankaya University, 06530, Balgat, Ankara, Turkey

    Dumitru Baleanu

  3. Data Recovery Key Laboratory of Sichuan Province, College of Mathematics and Information Science, Neijiang Normal University, Neijiang, 641100, P.R. China

    Guo-Cheng Wu

  4. Institute of Applied Nonlinear Science, College of Mathematics and Information Science, Neijiang Normal University, Neijiang, 641100, Sichuan, P.R. China

    Guo-Cheng Wu

Authors
  1. Fulai Chen
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  2. Dumitru Baleanu
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  3. Guo-Cheng Wu
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Correspondence to Dumitru Baleanu.

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Chen, F., Baleanu, D. & Wu, GC. Existence results of fractional differential equations with Riesz–Caputo derivative. Eur. Phys. J. Spec. Top. 226, 3411–3425 (2017). https://doi.org/10.1140/epjst/e2018-00030-6

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  • DOI: https://doi.org/10.1140/epjst/e2018-00030-6

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