Stability analysis of fractional differential equations with unknown parameters

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 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.

Existence and finite-time stability of solutions for a class of nonlinear fractional differential equations with time-varying delays and non-instantaneous impulses

“…An interesting extension of our study would be to discuss the stability with unknown parameters [37] and Ulam stability [20,43] for the ψ-Hilfer fractional differential equations with time-varying delay terms. This topic will be the subject of a forthcoming paper.…”

“…In [20], Ameen et al studied the Ulam stability and existence theorems for Caputo generalized fractional differential equations where the kernel of the fractional derivative was function dependent so that the result generalized many existing results in history. Further, for more details about some other properties of the solutions, we can see [28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43].…”

Stability analysis of fractional-order systems with randomly time-varying parameters

“…Fractional stochastic differential systems often arise in applications [1,3,7,13,22,26,30]. In recent years, such systems have attracted more and more researchers' attention in the field of stochastic differential systems.…”

Stability analysis of the hiv model through incommensurate fractional-order nonlinear system

“…According to the derivative-orders in the system, FOSs can be considered in two parts commensurate and incommensurate and commensurate FOSs is a special case of incommensurate FOSs. Therefore, studies on incommensurate FOSs as in [40][41][42][43][44][45][46][47][48][49][50][51][52] are increasingly included in the literature.…”