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Existence and U-H-R Stability of Solutions to the Implicit Nonlinear FBVP in the Variable Order Settings

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  • Mohammed K. A. Kaabar

    (Institute of Mathematical Sciences, Faculty of Science, University of Malaya, Kuala Lumpur 50603, Malaysia
    These authors contributed equally to this work.)

  • Ahmed Refice

    (Laboratory of Mathematics, Djillali Liabes University of Sidi Bel-Abbes, Sidi bel Abbes 22000, Algeria
    These authors contributed equally to this work.)

  • Mohammed Said Souid

    (Department of Economic Sciences, University of Tiaret, Tiaret 14035, Algeria
    These authors contributed equally to this work.)

  • Francisco Martínez

    (Department of Applied Mathematics and Statistics, Technological University of Cartagena, 30203 Cartagena, Spain
    These authors contributed equally to this work.)

  • Sina Etemad

    (Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 53751-71379, Iran
    These authors contributed equally to this work.)

  • Zailan Siri

    (Institute of Mathematical Sciences, Faculty of Science, University of Malaya, Kuala Lumpur 50603, Malaysia
    These authors contributed equally to this work.)

  • Shahram Rezapour

    (Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 53751-71379, Iran
    Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 406040, Taiwan
    These authors contributed equally to this work.)

Abstract

In this paper, the existence of the solution and its stability to the fractional boundary value problem (FBVP) were investigated for an implicit nonlinear fractional differential equation (VOFDE) of variable order. All existence criteria of the solutions in our establishments were derived via Krasnoselskii’s fixed point theorem and in the sequel, and its Ulam–Hyers–Rassias (U-H-R) stability is checked. An illustrative example is presented at the end of this paper to validate our findings.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:14:p:1693-:d:596905
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    References listed on IDEAS

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    1. Sun, HongGuang & Chen, Wen & Chen, YangQuan, 2009. "Variable-order fractional differential operators in anomalous diffusion modeling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(21), pages 4586-4592.
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    Cited by:

    1. Ashish Rayal & Bhagawati Prasad Joshi & Mukesh Pandey & Delfim F. M. Torres, 2023. "Numerical Investigation of the Fractional Oscillation Equations under the Context of Variable Order Caputo Fractional Derivative via Fractional Order Bernstein Wavelets," Mathematics, MDPI, vol. 11(11), pages 1-22, May.
    2. 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).

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