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

Date
2019-11-07
Authors
Stamov, Gani
Martynyuk, Anatoliy
Stamova, Ivanka
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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.

Description
Keywords
fractional-like derivative, impulses, practical stability, boundedness, h-manifolds
Citation
Fractal and Fractional 3 (4): 50 (2019)
Department
Mathematics