Mathematical applications of Ulam–Hyers stability in fractional hybrid differential systems

This study investigates the existence of solutions for a system of hybrid fractional differential equations governed by the generalized Hilfer fractional derivative, subject to nonlocal integral boundary conditions. The existence of solutions is thoroughly analyzed using Mönch’s fixed point theorem,...

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Published inJournal of applied mathematics & computing Vol. 71; no. 3; pp. 4025 - 4042
Main Authors Bawaneh, Sameer, Murugesan, Manigandan, Alahmadi, Jihan, Awadalla, Muath
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Nature B.V 01.06.2025
Subjects
Boundary conditions
Derivatives
Differential equations
Fixed points (mathematics)
Fractional calculus
Integrals
Stability criteria
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ISSN1598-5865
1865-2085
DOI10.1007/s12190-025-02391-6

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Summary:This study investigates the existence of solutions for a system of hybrid fractional differential equations governed by the generalized Hilfer fractional derivative, subject to nonlocal integral boundary conditions. The existence of solutions is thoroughly analyzed using Mönch’s fixed point theorem, providing a solid analytical foundation. Additionally, we utilize the Ulam–Hyers stability criterion to examine the stability properties of these solutions, ensuring the validity of our results. Finally, to demonstrate the practical relevance of the theoretical findings, we present a numerical example that showcases the applicability of the derived solutions.
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ISSN:1598-5865
1865-2085
DOI:10.1007/s12190-025-02391-6