4.7 Article

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

Journal

NONLINEAR DYNAMICS
Volume 107, Issue 4, Pages 3749-3766

Publisher

SPRINGER
DOI: 10.1007/s11071-021-07138-z

Keywords

Hadamard fractional calculus; Finite-time stability; Weighted Banach spaces; Beesack inequality; Delayed Mittag-Leffler matrix function

Funding

  1. National Natural Science Foundation of China [11902108]
  2. Natural Science Foundation of Anhui Province [1908085QA12]
  3. Fundamental Research Funds for the Central Universities of China [JZ2021HGTB0125]

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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.
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.

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