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Existence and uniqueness results for fractional boundary value problems with multiple orders of fractional derivatives and integrals

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  • Kherraz, Tahar
  • Benbachir, Maamar
  • Lakrib, Mustapha
  • Samei, Mohammad Esmael
  • Kaabar, Mohammed K.A.
  • Bhanotar, Shailesh A.

Abstract

In this article, we study boundary value problems for fractional differential equations with multiple orders of fractional derivatives and integrals, in both fractional differential equation and boundary conditions. Existence and uniqueness results are obtained using Sadovskii’s fixed point theorem. Finally, numerical examples are provided to confirm the applicability of obtained theoretical results.

Suggested Citation

  • Kherraz, Tahar & Benbachir, Maamar & Lakrib, Mustapha & Samei, Mohammad Esmael & Kaabar, Mohammed K.A. & Bhanotar, Shailesh A., 2023. "Existence and uniqueness results for fractional boundary value problems with multiple orders of fractional derivatives and integrals," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    • Handle: RePEc:eee:chsofr:v:166:y:2023:i:c:s0960077922011869
    DOI: 10.1016/j.chaos.2022.113007
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    References listed on IDEAS

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    1. Mohammed K. A. Kaabar & Ahmed Refice & Mohammed Said Souid & Francisco Martínez & Sina Etemad & Zailan Siri & Shahram Rezapour, 2021. "Existence and U-H-R Stability of Solutions to the Implicit Nonlinear FBVP in the Variable Order Settings," Mathematics, MDPI, vol. 9(14), pages 1-17, July.
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    Cited by:

    1. Haddouchi, Faouzi & Samei, Mohammad Esmael, 2024. "Solvability of a generalized ψ-Riemann–Liouville fractional BVP under nonlocal boundary conditions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 219(C), pages 355-377.

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