Finite-time stability of Hadamard fractional differential equations in weighted Banach spaces

Abstract

The main purpose of this paper is to investigate the finite-time stability of Hadamard fractional differential equations (HFDEs). Firstly, the standard definition of finite-time stability of HFDEs in compatible Banach space are proposed. In light of the method of successive approximation and Beesack inequality with weakly singular kernel, the criteria for finite-time stability of linear and nonlinear HFDEs are established, respectively. Then with regard to linear HFDEs with pure delay, a novel fractional delayed matrix function (also called delayed Mittag-Leffler matrix function) is given. Specific to nonlinear HFDEs with constant time delay, both Beesack inequality and Hölder inequality are utilized in the framework of the generalized Lipschitz condition. Finally, several indispensable simulations are implemented to verify the effectiveness and practicability of the main results.

Lyapunov Direct Method for Nonlinear Hadamard-Type Fractional Order Systems

“…It should be note that Li et al [19] investigated the logarithmic decay of fractional Hadamard and Caputo-Hadamard systems. Ma et al [30] discussed the finite-time stability of Hadamard-type systems.…”