Exponential form for Lyapunov function and stability analysis of the fractional differential equations

Volume 18, Issue 4, pp 388--397 http://dx.doi.org/10.22436/jmcs.018.04.01 Publication Date: October 25, 2018       Article History


Ndolane Sene - Laboratoire Lmdan, Departement de Mathematiques de la Decision, Faculte des Sciences Economiques et Gestion, Universite Cheikh Anta Diop de Dakar, BP 5683 Dakar Fann, Senegal.


This paper deals with an exponential form for Lyapunov function, in perspective to analyze the Lyapunov characterization of the Mittag-Leffler stability and the asymptotic stability for the fractional differential equations. In addition, a new Lyapunov characterization of Mittag-Leffler stability for fractional differential equations will be introduced. The exponential form will be used to prove the Lyapunov characterization of several stability notions, used in fractional differential equations. In this paper, the Caputo fractional derivative operator will be used to do the studies.