The practical stability of a nonlinear nonautonomous Caputo fractional differential equation is studied using Lyapunov like functions. The novelty of this paper is based on the new definition of the derivative of a Lyapunov like function along the given fractional differential equation. Comparison results using this definition for scalar fractional differential equations are presented. Several ...

In the paper the problem of practical stability of linear positive discrete-time systems of fractional order is addressed. New simple necessary and sufficient conditions for practical stability and for practical stability independent of the length of practical implementation are established. It is shown that practical stability of the system is equivalent to asymptotic stability of the correspo...

This article investigates the practical exponential stability and design problems of conformable time-delay systems. Sufficient conditions that confirm proposed class systems are given by utilizing an adequate Lyapunov–Krasovskii functional (L-KF). These expressed in form linear matrix inequalities (LMI) which could be solved using solvers LMI Toolbox MATLAB. Two numerical examples to illustrat...

This work is devoted to practical stability of a class of regime-switching diffusions. First, the notion of practical stability is introduced. Then, sufficient conditions for practical stability and practical instability in probability and in pth mean are provided using a Lyapunov function argument. In addition, easily verifiable conditions on drift and diffusion coefficients are also given. Mo...