Journal ArticleDOI
Dynamic analysis of a fractional-order Lorenz chaotic system
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In this paper, the existence and uniqueness of solutions for a class of fractional-order Lorenz chaotic systems are investigated theoretically, and the stability of the corresponding equilibria is also argued similarly to the integer-order counterpart.Abstract:
The dynamic behaviors of fractional-order differential systems have received increasing attention in recent decades. But many results about fractional-order chaotic systems are attained only by using analytic and numerical methods. Based on the qualitative theory, the existence and uniqueness of solutions for a class of fractional-order Lorenz chaotic systems are investigated theoretically in this paper. The stability of the corresponding equilibria is also argued similarly to the integer-order counterpart. According to the obtained results, the bifurcation conditions of these two systems are significantly different. Numerical solutions, together with simulations, finally verify the correctness of our analysis.read more
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A survey on the stability of fractional differential equations - Dedicated to Prof. Y.S. Chen on the Occasion of his 80th Birthday
TL;DR: A brief overview on the recent stability results of fractional differential equations and the analytical methods used are provided in this paper, where some conclusions for stability are similar to that of classical integer-order differential equations.
Journal ArticleDOI
Synchronization of fractional order chaotic systems using active control method
TL;DR: In this article, the active control method is used for synchronization of two different pairs of fractional order systems with Lotka-Volterra chaotic system as the master system and the other two fractional-order chaotic systems, viz., Newton-Leipnik and Lorenz systems as slave systems separately.
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Chaos in fractional-order Genesio–Tesi system and its synchronization
TL;DR: Theoretically, a necessary condition for occurrence of chaos is obtained and it is shown that in case of commensurate system the lowest order of fractional-order Genesio–Tesi system to yield chaos is 2.79.
Journal ArticleDOI
Bifurcations and Chaos in Fractional-Order Simplified Lorenz System
TL;DR: This paper numerically study the bifurcations and chaotic behaviors in the fractional-order simplified Lorenz system using the time-domain scheme and presents complex dynamics with interesting characteristics.
Journal ArticleDOI
Statements on chaos control designs, including a fractional order dynamical system, applied to a “MEMS” comb-drive actuator
Angelo Marcelo Tusset,José Manoel Balthazar,Dailhane G. Bassinello,B. R. Pontes,Jorge Luis Palacios Felix +4 more
TL;DR: In this article, three control strategies are used for controlling the trajectory of the system: state dependent Riccati Equation (SDRE), optimal linear feedback control, and fuzzy sliding mode control.
References
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Applications Of Fractional Calculus In Physics
TL;DR: An introduction to fractional calculus can be found in this paper, where Butzer et al. present a discussion of fractional fractional derivatives, derivatives and fractal time series.
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Analysis of Fractional Differential Equations
Kai Diethelm,Neville J. Ford +1 more
TL;DR: In this paper, the authors discuss existence, uniqueness, and structural stability of solutions of nonlinear differential equations of fractional order, and investigate the dependence of the solution on the order of the differential equation and on the initial condition.
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Fractional quantum mechanics and Lévy path integrals
TL;DR: In this article, a new extension of a fractality concept in quantum physics has been developed and path integrals over the Levy paths are defined and fractional quantum and statistical mechanics have been developed via new fractional path integral approach.