scholarly journals On the Stability of Linear Incommensurate Fractional-Order Difference Systems

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1754
Author(s):  
Noureddine Djenina ◽  
Adel Ouannas ◽  
Iqbal M. Batiha ◽  
Giuseppe Grassi ◽  
Viet-Thanh Pham
Keyword(s):  
Fractional Order ◽  
Difference Equations ◽  
Equivalent System ◽  
Stability Of Solutions ◽  
Extended Version ◽  
Transform Method ◽  
Order Difference ◽  
Difference Systems ◽  
The Stability

To follow up on the progress made on exploring the stability investigation of linear commensurate Fractional-order Difference Systems (FoDSs), such topic of its extended version that appears with incommensurate orders is discussed and examined in this work. Some simple applicable conditions for judging the stability of these systems are reported as novel results. These results are formulated by converting the linear incommensurate FoDS into another equivalent system consists of fractional-order difference equations of Volterra convolution-type as well as by using some properties of the Z-transform method. All results of this work are verified numerically by illustrating some examples that deal with the stability of solutions of such systems.

On the asymptotic stability of linear system of fractional-order difference equations

2013 ◽  
Vol 16 (3) ◽  
Author(s):  
Raghib Abu-Saris ◽  
Qasem Al-Mdallal
Keyword(s):  
Asymptotic Stability ◽  
Linear System ◽  
Fractional Order ◽  
Difference Equations ◽  
Equilibrium Solution ◽  
Initial Condition ◽  
System Of Difference Equations ◽  
Order Difference ◽  
Order Linear ◽  
The Stability

AbstractIn this paper we investigate the stability of the equilibrium solution of the νth order linear system of difference equations $(\Delta _{a + \nu - 1}^\nu y)(t) = \Lambda y(t + \nu - 1);t \in \mathbb{N}_a ,a \in \mathbb{R},and\Lambda \in \mathbb{R}^{p \times p} ,$ subject to the initial condition $y(a + \nu - 1) = y - 1,$, where 0 < ν < 1 and y−1 ∈ ℝp.

scholarly journals Novel convenient conditions for the stability of nonlinear incommensurate fractional-order difference systems

2021 ◽  
Author(s):  
Mohd Taib Shatnawi ◽  
Noureddine Djenina ◽  
Adel Ouannas ◽  
Iqbal M. Batiha ◽  
Giuseppe Grassi
Keyword(s):  
Fractional Order ◽  
Order Difference ◽  
Difference Systems ◽  
The Stability

On the Necessary and Sufficient Conditions for the Stability of Linear Generalized Ordinary Differential, Linear Impulsive and Linear Difference Systems

2009 ◽  
Vol 16 (4) ◽  
pp. 597-616
Author(s):  
Shota Akhalaia ◽  
Malkhaz Ashordia ◽  
Nestan Kekelia
Keyword(s):  
Linear System ◽  
Difference Equations ◽  
Closed Interval ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Difference Systems ◽  
The Stability ◽  
Necessary And Sufficient ◽  
Generalized Ordinary Differential Equations ◽  
Lyapunov Sense

Abstract Necessary and sufficient conditions are established for the stability in the Lyapunov sense of solutions of a linear system of generalized ordinary differential equations 𝑑𝑥(𝑡) = 𝑑𝐴(𝑡) · 𝑥(𝑡) + 𝑑𝑓(𝑡), where and are, respectively, matrix- and vector-functions with bounded total variation components on every closed interval from . The results are realized for the linear systems of impulsive, ordinary differential and difference equations.

scholarly journals Oscillation Results for a Class of Nonlinear Fractional Order Difference Equations with Damping Term

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
A. George Maria Selvam ◽  
Jehad Alzabut ◽  
Mary Jacintha ◽  
Abdullah Özbekler
Keyword(s):  
Fractional Order ◽  
Difference Equations ◽  
Difference Operator ◽  
Fractional Operators ◽  
Damping Term ◽  
Fractional Difference ◽  
Riccati Technique ◽  
Order Difference ◽  
Numerical Examples ◽  
Positive Integers

The paper studies the oscillation of a class of nonlinear fractional order difference equations with damping term of the form Δψλzηλ+pλzηλ+qλF∑s=λ0λ−1+μ λ−s−1−μys=0, where zλ=aλ+bλΔμyλ, Δμ stands for the fractional difference operator in Riemann-Liouville settings and of order μ, 0<μ≤1, and η≥1 is a quotient of odd positive integers and λ∈ℕλ0+1−μ. New oscillation results are established by the help of certain inequalities, features of fractional operators, and the generalized Riccati technique. We verify the theoretical outcomes by presenting two numerical examples.

Chaos in fractional-order difference systems

2022 ◽  
pp. 257-286
Author(s):  
Amina-Aicha Khennaoui ◽  
Adel Ouannas ◽  
Iqbal M. Batiha ◽  
Viet-Thanh Pham
Keyword(s):  
Fractional Order ◽  
Order Difference ◽  
Difference Systems

scholarly journals Full-order observers for linear fractional multi-order difference systems

2017 ◽  
Vol 65 (6) ◽  
pp. 891-898 ◽  
Author(s):  
M. Wyrwas
Keyword(s):  
Sufficient Condition ◽  
Transform Method ◽  
Order Difference ◽  
Numerical Examples ◽  
Difference Systems

AbstractThe paper is devoted to the construction of observers for linear fractional multi–order difference systems with Riemann–Liouville– and Grünwald–Letnikov–type operators. Basing on the Z-transform method the sufficient condition for the existence of the presented observers is established. The behaviour of the constructed observer is demonstrated in numerical examples.

scholarly journals Fractional Order Difference Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
J. Jagan Mohan ◽  
G. V. S. R. Deekshitulu
Keyword(s):  
Difference Equation ◽  
Fractional Order ◽  
Difference Equations ◽  
Existence And Uniqueness ◽  
Uniqueness Of Solutions ◽  
Fractional Difference ◽  
Order Difference ◽  
Fractional Difference Equations ◽  
Independent Variable

A difference equation is a relation between the differences of a function at one or more general values of the independent variable. These equations usually describe the evolution of certain phenomena over the course of time. The present paper deals with the existence and uniqueness of solutions of fractional difference equations.

Sign in / Sign up

Export Citation Format

Share Document