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ABSTRACT
This paper investigates the finite-time stability problem of a class of nonlinear fractional-order system with the discrete time delay. Employing the Laplace transform, the Mittag-Leffler function and the generalised Gronwall inequality, the new criterions are derived to guarantee the finite-time stability of the system with the fractional-order 0 < α < 1. Further, we propose the sufficient conditions for ensuring the finite-time stability of the system with the fractional-order 1 < α < 2. Finally, based on the modified Adams–Bashforth–Moulton algorithm for solving fractional-order differential equations with the time delay, we carry out the numerical simulations to demonstrate the effectiveness of the proposed results, and calculate the estimated time of the finite-time stability.
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Notes on contributors
Feifei Wang
Feifei Wang received her B.Sc. degree in Hydraulic and Hydro-power Engineering from Zhengzhou University, China in 2014. Now, she is a Ph.D. student of Hydraulic Engineering in Northwest A&F University, China. Her current research interests include nonlinear system stability, fractional-order system, time delay system and stability of hydropower.
Diyi Chen
Diyi Chen received his B.Sc. degree in electrical engineering and automation in 2005 from China University of Mining and Technology, China; his M.Sc. degree in theory and new technology of electrical engineering in 2008 from Shandong University, China and his Ph.D. degree in electrical engineering and automation in 2013 from Northwest A&F University, China. Dr Chen joined the Department of Electrical Engineering, Northwest A&F University as a lecturer in 2008. He is currently an associate professor at the same school. His research interests include nonlinear dynamics, stability and control of nonlinear systems, fractional calculus and its applications. He has published over 50 papers in these areas. He served as a visiting scholar at School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, AZ, USA from 27 July 2012 to 29 July 2013 and a visiting scholar at Department of Mathematics and Statistics, Curtin University, Australia from 2 October 2015 to 29 September 2016.
Xinguang Zhang
Xinguang Zhang received his Ph.D. degree in Qufu Normal University in Applied Mathematics in 2007, and worked as a professor in Yantai University. Now, he is a research fellow of Department of Mathematics and Statistics, Curtin University of Technology, Australia. Dr Zhang's major fields of interest are nonlinear analysis on manifolds, singular fractional-order differential equations, partial differential equation, singular or degenerate nonlinear evolution equations, mathematical models of fluid dynamics, variational methods, critical points theory. He has published over 60 research articles in applied mathematics. He is a member of the editorial board of several international journals.
Yonghong Wu
Yonghong Wu received his Ph.D. degree from the University of Wollongong in 1990, and continued there as an Australian national postdoctoral fellow, and then moved on to the University of New South Wales as a research scientist. In January 1993, he joined the department as a lecturer and progressed through senior lecturer, associate professor and became professor in December 2008. Prof Wu's research interests include computational mathematics (finite element method, boundary element method, optimisation of boundary value problems); applied mathematical modelling (fluid dynamics and heat transfer, granular flow, geomechanics) theory. He has published over 100 papers in these areas.