A class of fractional order systems with not instantaneous impulses
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Authors
Xianmin Zhang
- School of Mathematics and statistics, Yangtze Normal University, Fuling, Chongqing 408100, China.
Abstract
This paper is concerned with a kind of fractional order systems with Caputo-Hadamard derivative (of order \(q\in\mathbb{C}\) and \(\Re(q)\in(1,2)\)) and not instantaneous impulses. The obtained result uncovers that there exists a general solution for these impulsive systems, which means that the state trajectory of these impulsive systems is non-unique, and it is expounded by a numerical example.
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ISRP Style
Xianmin Zhang, A class of fractional order systems with not instantaneous impulses, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 8, 4398--4407
AMA Style
Zhang Xianmin, A class of fractional order systems with not instantaneous impulses. J. Nonlinear Sci. Appl. (2017); 10(8):4398--4407
Chicago/Turabian Style
Zhang, Xianmin. "A class of fractional order systems with not instantaneous impulses." Journal of Nonlinear Sciences and Applications, 10, no. 8 (2017): 4398--4407
Keywords
- Fractional differential equations
- impulsive fractional differential equations
- not instantaneous impulses
- general solution
- state trajectory.
MSC
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