in this paper, we introduce a family of fractional-order chebyshev functions based on the classical chebyshev polynomials. we calculate and derive the operational matrix of derivative of fractional order $gamma$ in the caputo sense using the fractional-order chebyshev functions. this matrix yields to low computational cost of numerical solution of fractional order differential equations to the ...

In recent years, there has been greater attempt to find numerical solutions of differential equations using wavelet's methods. The following method is based on vector forms of Haar-wavelet functions. In this paper, we will introduce one dimensional Haar-wavelet functions and the Haar-wavelet operational matrices of the fractional order integration. Also the Haar-wavelet operational matrices of ...

In this study, we propose a secure communication scheme based on the synchronization of two identical fractional-order chaotic systems. The fractional-order derivative is in Caputo sense, and for synchronization, we use a robust sliding-mode control scheme. The designed sliding surface is taken simply due to using special technic for fractional-order systems. Also, unlike most manuscripts, the ...

This paper presents a novel robust fractional PIλ controller design for flexible joint electrically driven robots. Because of using voltage control strategy, the proposed approach is free of problems arising from torque control strategy in the design and implementation. In fact, the motor's current includes the effects of nonlinearities and coupling in the robot manipulator. Therefore, cancella...

In this paper, a new approach to stability for fractional order control system is proposed. Here a dynamic system whose behavior can be modeled by means of differential equations involving fractional derivatives. Applying Laplace transforms to such equations, and assuming zero initial conditions, causes transfer functions with no integer powers of the Laplace transform variable s to appear. In ...

The aim of this work is to describe the qualitative behavior of the solution set of a given system of fractional differential equations and limiting behavior of the dynamical system or flow defined by the system of fractional differential equations. In order to achieve this goal, it is first necessary to develop the local theory for fractional nonlinear systems. This is done by the extension of...