Abstract. In this paper, the chaotic dynamics of a three-dimensional fractional-order chaotic system is investigated. The lowest order for exhibiting chaos in the fractional-order system is obtained. Adaptive schemes are proposed for control and synchronization of the fractional-order chaotic system based on the stability theory of fractional-order dynamic systems. The presented schemes, which ...

A new fractional-order chaotic system is proposed in this paper, and a list of state trajectories is presented with fractional derivative of different areas. Furthermore, a circuit diagram is studied to realize the fractional-order chaotic system. The new fractional-order chaotic system can be controlled to reach synchronization based on the nonlinear control theory, and the results between num...

in this paper, we investigate the existence of solution for a k-dimensional system of three points nabla fractional finite difference equations. also, we present an example to illustrate our result.

this paper studies the existence of solutions for acoupled system of nonlinear fractional differential equations. newexistence and uniqueness results are established using banach fixedpoint theorem. other existence results are obtained using schaeferand krasnoselskii fixed point theorems. some illustrative examplesare also presented.

Fractional-order financial system introduced by W.-C. Chen 2008 displays chaotic motions at order less than 3. In this paper we have extended the nonlinear feedback control in ODE systems to fractional-order systems, in order to eliminate the chaotic behavior. The results are proved analytically by applying the Lyapunov linearization method and stability condition for fractional system. Moreove...

in this paper, operational matrices of riemann-liouville fractional integration and caputo fractional differentiation for shifted jacobi polynomials are considered. using the given initial conditions, we transform the fractional differential equation (fde) into a modified fractional differential equation with zero initial conditions. next, all the existing functions in modified differential equ...

in this paper, the sinc collocation method is proposed for solving linear and nonlinear multi-order fractional differential equations based on the new definition of fractional derivative which is recently presented by khalil, r., al horani, m., yousef, a. and sababeh, m. in a new definition of fractional derivative, j. comput. appl. math. 264 (2014), 65{70. the properties of sinc functions are ...

Aiming at the characteristics of permanent magnet synchronous motor (PMSM) such as strong coupling and nonlinearity, we propose a fractional-order control scheme for the speed control of PMSM system based on the analysis of the fractional calculus theory. The simulation is conducted by using Matlab / Simulink. Simulation results indicate that the fractional-order PI controller can improve the d...

Specifically setting a time delay fractional financial system as the study object, this paper proposes a single controller method to eliminate the impact of model uncertainty and external disturbances on the system. The proposed method is based on the stability theory of Lyapunov sliding-mode adaptive control and fractional-order linear systems. The controller can fit the system state within th...