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Existence and Ulam stability results for two orders neutral fractional differential equations

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Abstract

In this paper, we study the existence and uniqueness of mild solutions for a nonlinear neutral fractional differential equation with two orders of Caputo’s fractional derivative using the Krasnoselskii and Banach fixed point theorems. We establish four types of Ulam stability: Ulam–Hyers, Ulam–Hyers–Rassias, generalized Ulam–Hyers and generalized Ulam–Hyers–Rassias. Two examples are given to substantiate the usefulness of the obtained results.

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Acknowledgements

The authors are grateful to the referees for their valuable comments which have led to improvement of the presentation.

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Authors and Affiliations

  1. Ecole Normale Supérieure d’Enseignement Technologique, Azzaba, Skikda, Algeria

    Houssem Eddine Khochemane

  2. Department of Mathematics and Informatics, University of Souk-Ahras, 1553, 41000, Souk-Ahras, Algeria

    Abdelouaheb Ardjouni & Salah Zitouni

Authors
  1. Houssem Eddine Khochemane
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  2. Abdelouaheb Ardjouni
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  3. Salah Zitouni
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Khochemane, H.E., Ardjouni, A. & Zitouni, S. Existence and Ulam stability results for two orders neutral fractional differential equations. Afr. Mat. 33, 35 (2022). https://doi.org/10.1007/s13370-022-00970-5

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  • DOI: https://doi.org/10.1007/s13370-022-00970-5

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