Lyapunov Functions and Stability Analysis of Fractional-Order Systems

TL;DR

This paper introduces new estimates for fractional derivatives without singular kernels, providing a method to analyze the global stability of fractional-order systems, demonstrated through a fractional SEIR epidemic model.

Contribution

It offers novel inequalities for fractional derivatives and generalizes existing stability analysis methods for fractional-order systems.

Findings

Established new estimates for fractional derivatives without singular kernels.

Provided a method for global stability analysis of fractional-order systems.

Proved the global stability of a fractional SEIR epidemic model.

Abstract

This study presents new estimates for fractional derivatives without singular kernels defined by some specific functions. Based on obtained inequalities, we give a useful method to establish the global stability of steady states for fractional-order systems and generalize some works existing in the literature. Finally, we apply our results to prove the global stability of a fractional-order SEIR model with a general incidence rate.