Lyapunov Direct Method for Nonlinear Hadamard-Type Fractional Order Systems

Author:

Dai ChangpingORCID,Ma WeiyuanORCID

Abstract

In this paper, a rigorous Lyapunov direct method (LDM) is proposed to analyze the stability of fractional non-linear systems involving Hadamard or Caputo–Hadamard derivatives. Based on the characteristics of Hadamard-type calculus, several new inequalities are derived for different definitions. By means of the developed inequalities and modified Laplace transform, the sufficient conditions can be derived to guarantee the Hadamard–Mittag–Leffler (HML) stability of the systems. Lastly, two illustrative examples are given to show the effectiveness of our proposed results.

Funder

the Fundamental Research Funds for the Central Universities

Publisher

MDPI AG

Subject

Statistics and Probability,Statistical and Nonlinear Physics,Analysis

Reference44 articles.

1. Theory and aAplications of Fractional Differential Equations;Kilbas,2006

2. Applications of fractional differential equation;Rahimy;Appl. Math. Sci.,2010

3. New power law inequalities for fractional derivative and stability analysis of fractional order systems

4. Advances in Fractional Calculus;Sabatier,2007

5. Fractional Derivatives for Physicists and Engineers;Uchaikin,2013

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