In this paper, control of uncertain fractional-order financial chaotic system with input saturation and external disturbance is investigated. The unknown part of the input saturation as well as the system's unknown nonlinear function is approximated by a fuzzy logic system. To handle the fuzzy approximation error and the estimation error of the unknown upper bound of the external disturbance, f...

Referring to incommensurate and commensurate fractional systems, this article presents a new approach to investigate the coexistence of some synchronization types between non-identical systems characterized by different dimensions and different orders. In particular, the paper shows that complete synchronization (CS), anti-synchronization (AS) and inverse full state hybrid function projective s...

A family of the billiard-type systems with zero Lyapunov exponent is considered as an example of dynamics which is between the regular one and chaotic mixing. This type of dynamics is called “pseudochaos”. We demonstrate how the fractional kinetic equation can be introduced for the pseudochaos and how the main critical exponents of the fractional kinetics can be evaluated from the dynamics. Pro...

The aim of this paper is to introduce a new hyperchaotic complex Lorenz system. This hyperchaotic complex system is constructed by adding a linear controller to the second equation of the chaotic complex Lorenz system. The new system is a 7-dimensional continuous real autonomous hyperchaotic system. This system has hyperchaotic attractors and quasi-periodic solutions with three zero Lyapunov ex...

This paper is devoted to discussing the existence and uniqueness of weak solutions time-fractional elliptic equations having time-dependent variable coefficients. To obtain main result, our strategy combine Galerkin method, a basic inequality for fractional derivative convex Lyapunov candidate functions, Yoshida approximation sequence compactness argument.

*Correspondence: [email protected]; [email protected] 1Department of Applied Mathematics, Yanshan University, Qinhuangdao, 066001, China Full list of author information is available at the end of the article Abstract This paper is concerned with the global projective synchronization issue for fractional neural networks in the Mittag-Leffler stability sense. Firstly, a fractional-order differ...