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Mathematical Biosciences and Engineering

2022, Volume 19, Issue 6: 6234-6251. doi: 10.3934/mbe.2022291
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Research article

Differential equations of arbitrary order under Caputo-Fabrizio derivative: some existence results and study of stability

  • 1.
    Department of Mathematics, University of Tiaret, Tiaret, Algeria
  • 2.
    CITMAga, 15782 Santiago de Compostela, España
  • 3.
    Departamento de Estatística, Análise Matemática e Optimización, Facultade de Matemáticas, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, España

  • Academic Editor: Yang Kuang
  • Received: 29 October 2021 Revised: 31 March 2022 Accepted: 11 April 2022 Published: 18 April 2022

  • In this work, we consider the problem of the existence and uniqueness of solution, and also the simple existence of solution, for implicit differential equations of arbitrary order involving Caputo-Fabrizio derivative. The main tools for this study are contraction mapping principle and Schaefer's fixed point result. We also study the stability of the equations in the sense of Ulam-Hyers and also from the perspective of Ulam-Hyers-Rassias.

    Citation: Kadda Maazouz, Rosana Rodríguez-López. Differential equations of arbitrary order under Caputo-Fabrizio derivative: some existence results and study of stability[J]. Mathematical Biosciences and Engineering, 2022, 19(6): 6234-6251. doi: 10.3934/mbe.2022291

    Related Papers:

  • In this work, we consider the problem of the existence and uniqueness of solution, and also the simple existence of solution, for implicit differential equations of arbitrary order involving Caputo-Fabrizio derivative. The main tools for this study are contraction mapping principle and Schaefer's fixed point result. We also study the stability of the equations in the sense of Ulam-Hyers and also from the perspective of Ulam-Hyers-Rassias.


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