Stability for the Systems of Ordinary Differential Equations with Caputo Fractional Order Derivatives

Asad J.  Taher; Fadhel S.  Fadhel; Nabaa N.  Hasan

doi:10.24996/ijs.2022.63.4.31

Authors

Asad J. Taher Department of Mathematics, College of Science, Mustansiriyah University, Baghdad, Iraq
Fadhel S. Fadhel Department of Mathematics and Computer Applications, College of Science, Al-Nahrain University, Baghdad, Iraq https://orcid.org/0000-0002-8351-2153
Nabaa N. Hasan Department of Mathematics, College of Science, MustansiriyahUniversity, Baghdad, Iraq

DOI:

https://doi.org/10.24996/ijs.2022.63.4.31

Keywords:

Backstepping Method, Caputo Fractional Derivative, Fractional Differential Equations, Stability, Lyapunov Function

Abstract

Fractional calculus has paid much attention in recent years, because it plays an essential role in many fields of science and engineering, where the study of stability theory of fractional differential equations emerges to be very important. In this paper, the stability of fractional order ordinary differential equations will be studied and introduced the backstepping method. The Lyapunov function is easily found by this method. This method also gives a guarantee of stable solutions for the fractional order differential equations. Furthermore it gives asymptotically stable.