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The objective of this work is to define the fractional order PID and the approximation of the integral and derivation of fractional order to render the system from irrational to rational. The parameters of PID are determined by three methods. These fractional controllers have two parameters more than the conventional PID controller, two more specifications can be met, improving the performance of...
In recent years, prey–predator models appearing in various fields of mathematical biology have been proposed and studied extensively due to their universal existence and importance. In this paper, we introduce a fractional-order prey–predator model and deals with the mathematical behaviors of the model. The dynamical behavior of the system is investigated from the point of view of local stability...
This paper proposes a new method for the simulation of the fractional systems. It deals with the approximation methods of the fractional derivative. It compare the approximation based on Grünwald with Caputo approximation. The efficiency of each approximation methods in terms of execution time and quadratic error is evaluated for different differential orders and stepsize. The best approximation...
Application of fractional derivative in control problems such as sliding surface design in sliding mode control, training of MLP in neural networks, and parameters updating in model reference adaptive control is studied in this paper. Use of the fractional derivative increases possibility of improving the control performance by reducing the convergence time in the mentioned control problems. This...
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