Special Fractional-Order Map and Its Realization

Analogue Realization of Fractional-Order Dynamical Systems

As it results from many research works, the majority of real dynamical objects are fractional-order systems, although in some types of systems the order is very close to integer order. Application of fractional-order models is more adequate for the description and analysis of real dynamical systems than integer-order models, because their total entropy is greater than in integer-order models wi...

Analog Realization of Fractional Order Circuits

The operational matrix of fractional derivative of the fractional-order Chebyshev functions and its applications

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 ...

Realization of Fractional-Order Capacitors with Field-Effect Transistors

A novel and efficient approach to realize fractional-order capacitors is investigated in this paper. Meanwhile, a new approach which is more efficient for semiconductor implementation of fractional-order capacitors is proposed. The feasibility of the approach has been verified with the preliminary measured results. Keywords—Fractional-order, field-effect transistors, RC transmission lines.

Realization of Fractional Order Controllers by Using Multiple Tuning-Rules

Fractional order PID controller has two degrees of freedom more than the integer order PID controller,and it has better control performance. The paper briefly describes the fractional order PID controller, and through Ziegler-Nichols type tuning rules, Padula & Visioli tuning rules and tuning by minimization methods to achieve fractional order PID controllers respectively. Additionally, the Ous...