In the fractional calculus, one of the main challenges is to find suitable models which are
properly described by discrete derivatives with memory. Fractional Logistic map and …

Without decomposing complex-valued systems into real-valued systems, this paper
investigates existence, uniqueness, global Mittag-Leffler stability and global Mittag-Leffler …

Dynamics of discrete‐time neural networks have not been well documented yet in fractional‐
order cases, which is the first time documented in this manuscript. This manuscript is mainly …

Lyapunov method is a powerful tool for studying the stability of dynamic systems while
existing work mainly focuses on the asymptotic stability and rarely concerns the …

In this paper, a fractional-order higher-dimensional multicavity chaotic map is investigated in
the Caputo discrete delta's sense. The numerical formula of discrete fractional-order chaotic …

This paper addresses the issue of stability analysis of nabla fractional order systems, which
is crucial when applying fractional calculus to control problems in engineering applications …

Due to the restriction of practical systems in time or space, tempered fractional calculus
becomes more reasonable than the traditional fractional calculus. It is known that stability …

This article focuses on the conservativeness issue of the existing Lyapunov method for
linear time-invariant (LTI) nabla fractional-order systems and proposes a converse …

The classical Leibniz rule for the integer difference cannot be easily applicable for the
fractional counterpart. It further leads to a great difficulty in the calculation of the Lyapunov …

This paper focuses on the problem of stability analysis for Riemann–Liouville nabla
fractional order systems. On one hand, a useful comparison principle is built and then a …