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

Hicham Ait Mohammed, Safa M. Mirgani (), Brahim Tellab, Abdelkader Amara, Mohammed El-Hadi Mezabia, Khaled Zennir and Keltoum Bouhali
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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

Mathematics, 2025, vol. 13, issue 9, 1-25

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.

Keywords: iterative methods; fractional derivatives; integral equation; multi-term boundary value problem; energy and industry; stability analysis (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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