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Existence and uniqueness of well-posed fractional boundary value problem

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  • Yuanheng Wang
  • Barrira Jurrat
  • Muddasir Ejaz
  • Muhammad Azeem
  • M I Elashiry

Abstract

In this paper, the existence and uniqueness of solution for a fractional differential model involving well-posed boundary conditions and implicit fractional differential equation is considered. The desired goals are achieved by using Banach contraction principle and Scheafer’s fixed point theorem. To show the results applicability some examples are presented. The basic mathematical concept of well-posed fractional boundary value issues is investigated in this study. It dives into the existence and uniqueness of these difficulties, offering light on the conditions that allow for both practical and singular solutions. This study contributes to a better knowledge of fractional calculus and its applications in a variety of scientific and technical areas, giving significant insights for both scholars and practitioners.

Suggested Citation

  • Yuanheng Wang & Barrira Jurrat & Muddasir Ejaz & Muhammad Azeem & M I Elashiry, 2024. "Existence and uniqueness of well-posed fractional boundary value problem," PLOS ONE, Public Library of Science, vol. 19(5), pages 1-26, May.
    • Handle: RePEc:plo:pone00:0303848
    DOI: 10.1371/journal.pone.0303848
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    References listed on IDEAS

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    1. Hind Sweis & Omar Abu Arqub & Nabil Shawagfeh, 2023. "Fractional delay integrodifferential equations of nonsingular kernels: Existence, uniqueness, and numerical solutions using Galerkin algorithm based on shifted Legendre polynomials," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 34(04), pages 1-23, April.
    2. Xiaoliang Xie & Bingqi Xie & Jiaqi Cheng & Qi Chu & Thomas Dooling, 2021. "A simple Monte Carlo method for estimating the chance of a cyclone impact," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 107(3), pages 2573-2582, July.
    3. 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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