Qualitative Analysis and Simulation of Fractional Hybrid Boundary Value Problems in Orthogonal Cone Metric Spaces

Abstract

This article aims to advance the qualitative analysis of fractional hybrid boundary value problems (FHBVPs) involving Riemann–Liouville fractional derivatives of order 1 < y ≤ 2, with a focus on establishing the existence, uniqueness, and stability of solutions in a novel mathematical framework. By employing the extended Banach fixed point theorem within orthogonal cone metric spaces, we prove the existence and uniqueness of solutions for FHBVPs, generalizing prior results in standard metric spaces and Banach algebras [1, 2]. Additionally, we investigate Hyers–Ulam stability to ensure solution robustness against perturbations, addressing common methodological errors in prior studies [3]. Numerical simulations complement our theoretical findings, demonstrating the impact of fractional order and nonlinear terms on solution behavior. These results provide new insights into modeling complex dynamic systems with nonlocal and memory-dependent behaviors, applicable to fields such as viscoelasticity, fluid dynamics, and biological modeling.