Impulsive Fractional-Like Differential Equations: Practical Stability and Boundedness with Respect to <i>h</i>-Manifolds

Abstract

In this paper, an impulsive fractional-like system of differential equations is introduced. The notions of practical stability and boundedness with respect to h-manifolds for fractional-like differential equations are generalized to the impulsive case. For the first time in the literature, Lyapunov-like functions and their derivatives with respect to impulsive fractional-like systems are defined. As an application, an impulsive fractional-like system of Lotka−Volterra equations is considered and new criteria for practical exponential stability are proposed. In addition, the uncertain case is also investigated.

Keywords

• fractional-like derivative
• impulses
• practical stability
• boundedness
• <i>h</i>-manifolds