Stability Analysis of Fractional Differential Equations with Unknown Parameters

TL;DR

This paper introduces a graphical D-decomposition method for analyzing the stability of fractional differential equations with unknown parameters, providing a simple and reliable approach without complex mathematics.

Contribution

It presents a novel graphical stability analysis technique for FDEs with unknown parameters, avoiding complicated mathematical procedures.

Findings

The method accurately determines stability boundaries.

It effectively identifies stability regions for FDEs.

Simulation results confirm the method's simplicity and reliability.

Abstract

In this paper, the stability of fractional differential equations (FDEs) with unknown parameters is studied. FDEs bring many advantages to model the physical systems in the nature or man-made systems in the industry. Because this representation has a property between linear differential equations and nonlinear differential equations. Therefore, the designer may use the FDEs to model complex systems instead of nonlinear differential equations which have hard mathematical background. Using the graphical based D-decomposition method, we investigate the parametric stability analysis of FDEs without complicated mathematical analysis. To achieve this, stability boundaries are obtained firstly, and then the stability region set depending on the unknown parameters is found. The applicability of the presented method is shown considering some benchmark equations which are often used to verify the results of a new method. Simulation examples shown that the method is simple and give reliable stability results.