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A Fixed-Point Approach to the Hyers–Ulam Stability of Caputo–Fabrizio Fractional Differential Equations

Author

Listed:
  • Kui Liu

    (Department of Mathematics, Guizhou University, Guiyang 550025, China
    College of Science, Guizhou Institute of Technology, Guiyang 550025, China)

  • Michal Fečkan

    (Department of Mathematical Analysis and Numerical Mathematics, Faculty of Mathematics, Physics and Informatics, Comenius University in Bratislava, Mlynská dolina, 842 48 Bratislava, Slovakia
    Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, 814 73 Bratislava, Slovakia)

  • JinRong Wang

    (Department of Mathematics, Guizhou University, Guiyang 550025, China
    School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China)

Abstract

In this paper, we study Hyers–Ulam and Hyers–Ulam–Rassias stability of nonlinear Caputo–Fabrizio fractional differential equations on a noncompact interval. We extend the corresponding uniqueness and stability results on a compact interval. Two examples are given to illustrate our main results.

Suggested Citation

  • Kui Liu & Michal Fečkan & JinRong Wang, 2020. "A Fixed-Point Approach to the Hyers–Ulam Stability of Caputo–Fabrizio Fractional Differential Equations," Mathematics, MDPI, vol. 8(4), pages 1-12, April.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:4:p:647-:d:349027
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    References listed on IDEAS

    as
    1. Soon-Mo Jung & Themistocles M. Rassias, 2010. "A Fixed Point Approach to the Stability of a Logarithmic Functional Equation," Springer Optimization and Its Applications, in: Panos M. Pardalos & Themistocles M. Rassias & Akhtar A. Khan (ed.), Nonlinear Analysis and Variational Problems, chapter 0, pages 99-109, Springer.
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