Motivated by the importance of study on the complex behaviors, which may be exhibited by
fractional order differential equations, this review paper focuses on dynamical fractional …

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 …

The Riemann–Liouville fractional integral for repeated fractional integration is expanded in
block pulse functions to yield the block pulse operational matrices for the fractional order …

In this paper, a sliding mode control law is designed to control chaos in a class of fractional-
order chaotic systems. A class of unknown fractional-order systems is introduced. Based on …

This paper presents two different stabilization methods based on the fractional-calculus
theory. The first method is proposed via using the fractional differentiator, and the other is …

In this paper, we have considered a three-dimensional Lotka–Volterra attractor in the frame
of the Caputo fractional derivative to examine its dynamics. The theoretical concepts like …

The review was devoted to describing the dynamics of various systems and control
processes in terms of the fractional integro-differential calculus. Consideration was given to …

In this paper, a new four-variable dynamical system is proposed to set chaotic circuit
composed of memristor and Josephson junction, and the dependence of chaotic behaviors …

In general, a nonlinear system is a system which is not linear, that is, a system which does
not satisfy the superposition principle. In mathematics, a nonlinear system is any problem …

Nowadays, the control of fractional-order system is one of the most popular topics in control
theory. Recent studies have demonstrated the interest of fractional calculus both for systems …