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

The main purpose of this paper is to investigate the finite-time stability of Hadamard fractional differential equations (HFDEs). Firstly, the standard definitions of finite-time stability of HFDEs in compatible Banach spaces are proposed. In light of the method of successive approximation and Beesack inequality with weakly singular kernel, the criteria of finite-time stability for 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 Holder 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.

Automated summary

The main purpose of this paper is to investigate the finite-time stability of Hadamard fractional differential equations (HFDEs). The criteria of finite-time stability for linear and nonlinear HFDEs are established using the method of successive approximation and Beesack inequality with weakly singular kernel. A novel fractional delayed matrix function is given for linear HFDEs with pure delay, and both Beesack inequality and Holder inequality are utilized for nonlinear HFDEs with constant time delay. Several simulations are implemented to verify the effectiveness and practicability of the main results.