Generalization of fractional differential operators was subjected to an intense debate in the
last few years in order to contribute to a deep understanding of the behavior of complex …

The cable equation plays a central role in many areas of electrophysiology and in modeling
neuronal dynamics. This paper reports an accurate spectral collocation method for solving …

In this paper stability analysis of fractional-order nonlinear systems is studied. An extension
of Lyapunov direct method for fractional-order systems using Bihari's and Bellman …

This paper deals with optimization and design of an integer order–based and fractional
order–based proportional integral derivative (PID) controller tuned by particle swarm …

Stability as an extremely important property of dynamical systems can be investigated in
various domains (Bellman, 1953; Dorf and Bishop, 1990). The usual concept of the bounded …

One of the reasons of the great success of standard PID controllers is the presence of simple
tuning rules, of the automatic tuning feature and of tables that simplify significantly their …

Synchronization of fractional order chaotic dynamical systems is receiving increasing
attention owing to its interesting applications in secure communications of analog and digital …

In this paper, a novel fractional-order terminal sliding mode control approach is introduced to
control/synchronize chaos of fractional-order nonautonomous chaotic/hyperchaotic systems …

A novel approach to solve optimal control problems dealing simultaneously with fractional
differential equations and time delay is proposed in this work. More precisely, a set of global …

Fractional order controller design with a small number of tuning parameters is very attractive.
Few attempts have been done recently for some limited cases of models. In this paper, a …