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Fractal Fract
Volume 9
Issue 11
10.3390/fractalfract9110735
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Article

Study of a Coupled System of Integro-Differential Equations Involving the Generalized Proportional Caputo Derivatives

by
Shorog Aljoudi
*,
Hind Alamri
and
Manar Alrubaie
Department of Mathematics, Faculty of Sciences, Taif University, P.O. Box 888, Taif 21974, Saudi Arabia
*
Author to whom correspondence should be addressed.
Fractal Fract. 2025, 9(11), 735; https://doi.org/10.3390/fractalfract9110735 (registering DOI)
Submission received: 15 September 2025 / Revised: 1 November 2025 / Accepted: 11 November 2025 / Published: 13 November 2025
(This article belongs to the Special Issue Women’s Special Issue Series: Fractal and Fractional, 2nd Edition)
Versions Notes

Abstract

This paper deals with a new coupled system of integro-differential equations involving the generalized proportional Caputo derivatives equipped with nonlocal four-point boundary conditions. Sufficient criteria for the existence and uniqueness of solutions for the studied system are derived based on Krasnoselskii’s and Banach fixed-point theorems, respectively. Applications are constructed with three different cases to illustrate the main results.
Keywords: generalized proportional; Caputo fractional derivatives; fractional differential equations; nonlocal boundary conditions; fixed-point theorems generalized proportional; Caputo fractional derivatives; fractional differential equations; nonlocal boundary conditions; fixed-point theorems

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MDPI and ACS Style

Aljoudi, S.; Alamri, H.; Alrubaie, M. Study of a Coupled System of Integro-Differential Equations Involving the Generalized Proportional Caputo Derivatives. Fractal Fract. 2025, 9, 735. https://doi.org/10.3390/fractalfract9110735

AMA Style

Aljoudi S, Alamri H, Alrubaie M. Study of a Coupled System of Integro-Differential Equations Involving the Generalized Proportional Caputo Derivatives. Fractal and Fractional. 2025; 9(11):735. https://doi.org/10.3390/fractalfract9110735

Chicago/Turabian Style

Aljoudi, Shorog, Hind Alamri, and Manar Alrubaie. 2025. "Study of a Coupled System of Integro-Differential Equations Involving the Generalized Proportional Caputo Derivatives" Fractal and Fractional 9, no. 11: 735. https://doi.org/10.3390/fractalfract9110735

APA Style

Aljoudi, S., Alamri, H., & Alrubaie, M. (2025). Study of a Coupled System of Integro-Differential Equations Involving the Generalized Proportional Caputo Derivatives. Fractal and Fractional, 9(11), 735. https://doi.org/10.3390/fractalfract9110735

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