The paper presents development of a new tuning method for fractional order PID controller for the systems which have integer order transfer functions. All the parameters of the controller, namely proportional gain kp, integral gain ki, derivative gain kd, fractional order of integrator λ and fractional order of differentiator μ can be obtained by using this method. It is clearly shown that the ...

The numerical solution of a variable-order fractional financial system is calculated by using the Adams-Bashforth-Moulton method. The derivative is defined in the Caputo variable-order fractional sense. Numerical examples show that the Adams-Bashforth-Moulton method can be applied to solve such variable-order fractional differential equations simply and effectively. The convergent order of the ...

We present a general series representation formula for the local solution of Bernoulli equation with Caputo fractional derivatives. then focus on generalization logistic and some related numerical simulations.

the current paper contributes a novel framework for solving a class of linear matrix differential equations. to do so, the operational matrix of the derivative based on the shifted bernoulli polynomials together with the collocation method are exploited to reduce the main problem to system of linear matrix equations. an error estimation of presented method is provided. numerical experiments are...

in this article we implement an operational matrix of fractional integration for legendre polynomials. we proposed an algorithm to obtain an approximation solution for fractional differential equations, described in riemann-liouville sense, based on shifted legendre polynomials. this method was applied to solve linear multi-order fractional differential equation with initial conditions, and the...

The paper presents a new closed-form expression for the fractional Fourier transform of generalized Triangular and Welch window functions. Fractional Fourier Transform (FrFT) is a parameterized transform having an adjustable transform parameter which makes it more flexible and superior over ordinary Fourier transform in several applications. It is an important tool used in signal processing for...

‎in this paper, we investigate the chaotic behaviors of the fractional-order permanent magnet synchronous motor (pmsm) system. the necessary condition for the existence of chaos in the fractional-order pmsm system is deduced and an active controller is developed based on the stability theory for fractional systems. the presented control scheme  is simple and flexible, and it is suitable both fo...

In this paper we will prove certain Hadamard and Fejer-Hadamard inequalities for the functions whose nth derivatives are convex by using Caputo k-fractional derivatives. These results have some relationship with inequalities for Caputo fractional derivatives.