A new method of dynamical stability, i.e. fractional generalized Hamiltonian method, and its applications

Shao-Kai, Luo; He, Jin–Man

doi:10.1016/j.amc.2015.07.047

Cited by 10 publications

(2 citation statements)

References 44 publications

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“…Eshaghi et al (2020) investigated the stability and chaotic behaviors of a Caputo fractional order system with the chaos entanglement function. Some authors studied the stability of a dynamical system in terms of Riesz-Riemann-Liouville derivative by means of the generalized fractional Hamilton method and the fractional Birkhoffian method (Luo et al 2015(Luo et al , 2016a. Hu et al (2015) also surveyed the stabilization of nonlinear Caputo fractional systems without and with delay by using the Lyapunov stability theorem.…”

Section: Introductionmentioning

confidence: 99%

Stability and dynamics of neutral and integro-differential regularized Prabhakar fractional differential systems

2020

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In this work, we investigate the asymptotic stability analysis for two classes of nonlinear fractional systems with the regularized Prabhakar derivative. The stability analysis of the neutral and integro-differential nonlinear fractional systems are studied by assessing the eigenvalues of associated matrix and applying conditions on the nonlinear part of these types of systems. We use a numerical method to solve the fractional differential equations with the regularized Prabhakar fractional derivative. We further present the numerical simulations on several test cases to examine and reveal the complex dynamics of the analytical obtained results.

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Section: Introductionmentioning

confidence: 99%

Stability and dynamics of neutral and integro-differential regularized Prabhakar fractional differential systems

2020

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“…Fractional‐order system is more general than classical integer order system and it can provide an excellent instrument for the description of memory and hereditary properties of some materials and processes, which can more truly reveal the internal structure and dynamical behaviors of an actual system. In recent years, fractional dynamical method has been widely used in theoretical and applied aspects of numerous branches, such as applied mathematics, mechanics and physics problems, anomalous diffusion, optimal control, secure communication and encryption, heat conduction, and biological systems . They demonstrate the importance of fractional calculus and motivate the development of new applications.…”

Section: Introductionmentioning

confidence: 99%

Fractional matrix and inverse matrix projective synchronization methods for synchronizing the disturbed fractional‐order hyperchaotic system

Chen

Lei

2018

Math Methods in App Sciences

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In this paper, for synchronizing two actual nonidentical fractional-order hyperchaotic systems disturbed by model uncertainty and external disturbance, the fractional matrix and inverse matrix projective synchronization methods are presented and the methods' correctness and effectiveness are proved. Especially, under certain degenerative conditions, the methods are reduced to study the complete synchronization, antisynchronization, projective (or inverse projective) synchronization, modified (or modified inverse) projective synchronization, and stabilization problem for the disturbed (or undisturbed) fractional-order hyperchaotic systems. In addition, as the fractional matrix and inverse matrix projective synchronization methods' applications, the fractional-order hyperchaotic Chen and Rabinovich systems disturbed by model uncertainty and external disturbance are constructed, and the matrix and inverse matrix projective synchronizations between the two disturbed systems are achieved, respectively. This work constructs a basic theoretical framework of fractional matrix and inverse matrix projective synchronization methods and provides a general method for synchronizing the actual disturbed fractional-order hyperchaotic systems that are related to science and engineering. KEYWORDS disturbed hyperchaotic system, fractional inverse matrix projective synchronization, fractional matrix projective synchronization, fractional-order derivative Math Meth Appl Sci. 2018;41:6907-6920.wileyonlinelibrary.com/journal/mma

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A general method of fractional dynamics, i.e., fractional Jacobi last multiplier method, and its applications

Shao-Kai

Zhang

2016

Acta Mech

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A new method of dynamical stability, i.e. fractional generalized Hamiltonian method, and its applications

Cited by 10 publications

References 44 publications

Stability and dynamics of neutral and integro-differential regularized Prabhakar fractional differential systems

Stability and dynamics of neutral and integro-differential regularized Prabhakar fractional differential systems

Fractional matrix and inverse matrix projective synchronization methods for synchronizing the disturbed fractional‐order hyperchaotic system

A general method of fractional dynamics, i.e., fractional Jacobi last multiplier method, and its applications

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