Stability Analysis of Fractional Differential Equations with Unknown Parameters

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 nature or man-made systems in industry. In fact, real objects are generally fractional and fractional calculus has gained popularity in modelling physical and engineering systems in the last few decades in parallel to advancement of high speed computers. 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.