A novel approach for the stability analysis of a system of m -non linear fractional differential equations of arbitrary order

This paper introduces a novel methodology for examining the stability of \(m\)-nonlinear fractional differential equations of any order, with possible applications in engineering, biology, and finance. These equations frequently represent intricate systems exhibiting memory and hereditary characteristics, like diffusion processes, population dynamics, or viscoelastic materials. We demonstrate the existence and uniqueness of solutions using fixed-point theorems in fractional calculus. Schaefer's theorem guarantees the existence of solutions, but Banach's theorem affirms their uniqueness. Additionally, the system's stability is examined by Hyers-Ulam stability, offering insights into its response to minor disturbances. To substantiate the theoretical findings, two practical examples are shown, illustrating the efficacy of the suggested strategy in real-world contexts. This methodology provides a comprehensive framework for tackling stability in systems influenced by fractional dynamics, facilitating applications in science and engineering.