EXISTENCE, UNIQUENESS, AND STABILITY OF SOLUTIONS FOR NONLINEAR FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS WITH NONLOCAL BOUNDARY CONDITIONS AND FRACTIONAL DERIVATIVES

Mirvet Abou Omar; Yahia Awad; Ragheb Hatem Mghames; Karim Mohammad Amin

EXISTENCE, UNIQUENESS, AND STABILITY OF SOLUTIONS FOR NONLINEAR FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS WITH NONLOCAL BOUNDARY CONDITIONS AND FRACTIONAL DERIVATIVES

Abstract

This study investigates a nonlinear fractional integro-differential equation defined by Riemann-Liouville fractional derivatives, focusing on the existence, uniqueness, and stability of its solutions. Using advanced fixed-point theorems, specifically the Banach and Krasnoselskii's fixed-point theorems, we derive precise conditions for the existence and uniqueness of solutions. We also conduct a stability analysis, establishing criteria to ensure the robustness of solutions under minor perturbations. The theoretical results extend existing frameworks in fractional differential equations and provide novel insights into fractional dynamic systems. To validate our theoretical findings and demonstrate their practical applicability, we present a numerical example that illustrates the solution behavior under varying fractional orders, nonlinearities, and boundary conditions. This example highlights the effectiveness of the proposed methods and lays the foundation for future research on fractional integro-differential equations in real-world applications.

Keywords

Thanks

The authors extend their sincere thanks to the editors and reviewers for their invaluable feedback and contributions, which have greatly improved the quality and impact of the manuscript.

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Details

Primary Language

English

Subjects

Numerical Solution of Differential and Integral Equations, Ordinary Differential Equations, Difference Equations and Dynamical Systems

Journal Section

Research Article

Authors

Mirvet Abou Omar This is me
0009-0008-6787-0285
Lebanon

Yahia Awad ^*
0000-0001-9878-2482
Lebanon

Ragheb Hatem Mghames This is me
0000-0001-9459-8530
Lebanon

Karim Mohammad Amin This is me
0009-0001-3422-8244
Lebanon

Publication Date

October 1, 2025

Submission Date

November 3, 2024

Acceptance Date

December 20, 2024

Published in Issue

Year 2025 Volume: 15 Number: 10

IZ

https://izlik.org/JA76GC45BH

Cite

RIS / Bibtex

APA

Abou Omar, M., Awad, Y., Mghames, R. H., & Amin, K. M. (2025). EXISTENCE, UNIQUENESS, AND STABILITY OF SOLUTIONS FOR NONLINEAR FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS WITH NONLOCAL BOUNDARY CONDITIONS AND FRACTIONAL DERIVATIVES. TWMS Journal of Applied and Engineering Mathematics, 15(10), 2465-2488. https://izlik.org/JA76GC45BH

AMA

1.Abou Omar M, Awad Y, Mghames RH, Amin KM. EXISTENCE, UNIQUENESS, AND STABILITY OF SOLUTIONS FOR NONLINEAR FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS WITH NONLOCAL BOUNDARY CONDITIONS AND FRACTIONAL DERIVATIVES. JAEM. 2025;15(10):2465-2488. https://izlik.org/JA76GC45BH

Chicago

Abou Omar, Mirvet, Yahia Awad, Ragheb Hatem Mghames, and Karim Mohammad Amin. 2025. “EXISTENCE, UNIQUENESS, AND STABILITY OF SOLUTIONS FOR NONLINEAR FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS WITH NONLOCAL BOUNDARY CONDITIONS AND FRACTIONAL DERIVATIVES”. TWMS Journal of Applied and Engineering Mathematics 15 (10): 2465-88. https://izlik.org/JA76GC45BH.

EndNote

Abou Omar M, Awad Y, Mghames RH, Amin KM (October 1, 2025) EXISTENCE, UNIQUENESS, AND STABILITY OF SOLUTIONS FOR NONLINEAR FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS WITH NONLOCAL BOUNDARY CONDITIONS AND FRACTIONAL DERIVATIVES. TWMS Journal of Applied and Engineering Mathematics 15 10 2465–2488.

IEEE

[1]M. Abou Omar, Y. Awad, R. H. Mghames, and K. M. Amin, “EXISTENCE, UNIQUENESS, AND STABILITY OF SOLUTIONS FOR NONLINEAR FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS WITH NONLOCAL BOUNDARY CONDITIONS AND FRACTIONAL DERIVATIVES”, JAEM, vol. 15, no. 10, pp. 2465–2488, Oct. 2025, [Online]. Available: https://izlik.org/JA76GC45BH

ISNAD

Abou Omar, Mirvet - Awad, Yahia - Mghames, Ragheb Hatem - Amin, Karim Mohammad. “EXISTENCE, UNIQUENESS, AND STABILITY OF SOLUTIONS FOR NONLINEAR FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS WITH NONLOCAL BOUNDARY CONDITIONS AND FRACTIONAL DERIVATIVES”. TWMS Journal of Applied and Engineering Mathematics 15/10 (October 1, 2025): 2465-2488. https://izlik.org/JA76GC45BH.

JAMA

1.Abou Omar M, Awad Y, Mghames RH, Amin KM. EXISTENCE, UNIQUENESS, AND STABILITY OF SOLUTIONS FOR NONLINEAR FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS WITH NONLOCAL BOUNDARY CONDITIONS AND FRACTIONAL DERIVATIVES. JAEM. 2025;15:2465–2488.

MLA

Abou Omar, Mirvet, et al. “EXISTENCE, UNIQUENESS, AND STABILITY OF SOLUTIONS FOR NONLINEAR FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS WITH NONLOCAL BOUNDARY CONDITIONS AND FRACTIONAL DERIVATIVES”. TWMS Journal of Applied and Engineering Mathematics, vol. 15, no. 10, Oct. 2025, pp. 2465-88, https://izlik.org/JA76GC45BH.

Vancouver

1.Mirvet Abou Omar, Yahia Awad, Ragheb Hatem Mghames, Karim Mohammad Amin. EXISTENCE, UNIQUENESS, AND STABILITY OF SOLUTIONS FOR NONLINEAR FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS WITH NONLOCAL BOUNDARY CONDITIONS AND FRACTIONAL DERIVATIVES. JAEM [Internet]. 2025 Oct. 1;15(10):2465-88. Available from: https://izlik.org/JA76GC45BH