The fractional derivative holds long-time memory effects or non-locality. It successfully
depicts the dynamical systems with long-range interactions. However, it becomes …

In this paper, we firstly develop an inequality on the rising function, which help us to deal
with the fractional integral (sum) in terms of Hölder inequality. Secondly, a finite-time stability …

This work aims to present a study on the stability analysis of linear and nonlinear
incommensurate h-nabla fractional-order difference systems. Several theoretical results are …

We study two cases of nabla fractional Caputo difference equations. Our main tool used is a
Banach fixed pointtheorem, which allows us to give some existence and uniqueness …

This paper proposes fractional quantum Julia sets based on a fractional q-difference map
and preliminarily investigates their fractal dynamic characteristics by numerical methods and …

In this paper we study the half order nabla fractional difference equation ρ (a)∇ 0.5 hx (t)= cx
(t), t∈(hN) a+ h, where ρ (a)∇ 0.5 hx (t) denotes the Riemann-Liouville nabla half order h …

A new discrete fractional-order Peano-Baker series is established in this paper. Based on
this series, the explicit solutions of Caputo linear discrete fractional-order equations (DFOEs) …

In this paper, a generalized fractional (q, h)–Gronwall inequality is investigated. Based on
this inequality, the uniqueness theorem and the finite–time stability criterion of nonlinear …

This paper investigates stability of the nabla $(q, h) $-fractional difference equations.
Asymptotic stability of the special nabla $(q, h) $-fractional difference equations are …

In this article, an explicit solution of the homogeneous fractional delay oscillation difference
equation of order 1< ι< 2 1&lt; ι &lt; 2 is given by constructing discrete sine‐and cosine‐type …