Qualitative Analysis of a Three-Dimensional Dynamical System of Fractal-Fractional-Order Evolution Differential Equations with Terminal Boundary Conditions

In this research article, we investigate a three-dimensional dynamical system governed by fractal-fractional-order evolution differential equations subject to terminal boundary conditions. We derive existence and uniqueness results using Schaefer’s and Banach’s fixed-point theorems, respectively. Additionally, the Hyers–Ulam stability approach is employed to analyze the system’s stability. We employ vector terminology for the proposed problem to make the analysis simple. To illustrate the practical relevance of our findings, we apply the derived results to a numerical example and graphically illustrate the solution for different fractal-fractional orders, emphasizing the effect of the derivative’s order on system behavior.