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Hyers–Ulam Stability Results of Solutions for a Multi-Point φ -Riemann-Liouville Fractional Boundary Value Problem

Author

Listed:
  • Hicham Ait Mohammed

    (Applied Mathematics Laboratory, Kasdi Merbah University, BP511, Ouargla 30000, Algeria)

  • Safa M. Mirgani

    (Department of Mathematics and Statistics, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 13318, Saudi Arabia)

  • Brahim Tellab

    (Applied Mathematics Laboratory, Kasdi Merbah University, BP511, Ouargla 30000, Algeria)

  • Abdelkader Amara

    (Applied Mathematics Laboratory, Kasdi Merbah University, BP511, Ouargla 30000, Algeria)

  • Mohammed El-Hadi Mezabia

    (Applied Mathematics Laboratory, Kasdi Merbah University, BP511, Ouargla 30000, Algeria)

  • Khaled Zennir

    (Department of Mathematics, College of Science, Qassim University, Buraydah 52571, Saudi Arabia)

  • Keltoum Bouhali

    (Department of Mathematics, College of Science, Qassim University, Buraydah 52571, Saudi Arabia)

Abstract

In this study, we investigate the existence, uniqueness, and Hyers–Ulam stability of a multi-term boundary value problem involving generalized φ -Riemann–Liouville operators. The uniqueness of the solution is demonstrated using Banach’s fixed-point theorem, while the existence is established through the application of classical fixed-point theorems by Krasnoselskii. We then delve into the Hyers–Ulam stability of the solutions, an aspect that has garnered significant attention from various researchers. By adapting certain sufficient conditions, we achieve stability results for the Hyers–Ulam (HU) type. Finally, we illustrate the theoretical findings with examples to enhance understanding.

Suggested Citation

  • Hicham Ait Mohammed & Safa M. Mirgani & Brahim Tellab & Abdelkader Amara & Mohammed El-Hadi Mezabia & Khaled Zennir & Keltoum Bouhali, 2025. "Hyers–Ulam Stability Results of Solutions for a Multi-Point φ -Riemann-Liouville Fractional Boundary Value Problem," Mathematics, MDPI, vol. 13(9), pages 1-25, April.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:9:p:1450-:d:1644852
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    References listed on IDEAS

    as
    1. Thabet Abdeljawad, 2013. "On Delta and Nabla Caputo Fractional Differences and Dual Identities," Discrete Dynamics in Nature and Society, Hindawi, vol. 2013, pages 1-12, July.
    2. Badr Alqahtani & Andreea Fulga & Erdal Karapınar, 2018. "Fixed Point Results on Δ-Symmetric Quasi-Metric Space via Simulation Function with an Application to Ulam Stability," Mathematics, MDPI, vol. 6(10), pages 1-19, October.
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