January 1, 2025Open Access

Advanced Fixed Point Methods for Analyzing Coupled Caputo Q‐Fractional Boundary Value Problems With Supportive Examples

HHHasanen A. HammadQassim University SASaleh Fahad AljurbuaQassim University ALAsamh Saleh M. Al LuhaybQassim University

Key Points

Uniqueness and existence of solutions are addressed for coupled boundary value problems based on fixed-point theory, providing a robust framework.
Utilizing Banach's fixed-point theorem, the analysis confirms solution viability in complex systems of fractional discrete equations.
Multiple worked examples illustrate the applicability of the proposed analytical methods, showcasing their real-world relevance.
The findings advance methodologies for addressing fractional boundary value problems, indicating potential applications across various fields.

Abstract

This article analyzes a complex coupled system of multipoint nonlinear boundary value problems involving Caputo‐type fractional discrete differential equations with multiple fractional q −integrals. We establish the uniqueness and existence of solutions using a rigorous approach grounded in fixed‐point theory, specifically Banach’s fixed‐point theorem and the Leray–Schauder theorem. The theoretical findings are supported by several concrete examples, demonstrating the practical applicability of the developed analytical techniques and advancing solution methodologies for fractional discrete boundary value problems.

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