On Mittag–Leffler Stability of Fractional Order Difference Systems

2015 ◽  
pp. 209-220 ◽  
Author(s):  
Małgorzata Wyrwas ◽  
Dorota Mozyrska
Keyword(s):  
Fractional Order ◽  
Order Difference ◽  
Difference Systems

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 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.

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

scholarly journals Chaos in the discrete memristor-based system with fractional-order difference

2021 ◽  
Vol 24 ◽  
pp. 104106
Author(s):  
Yuexi Peng ◽  
Shaobo He ◽  
Kehui Sun
Keyword(s):  
Fractional Order ◽  
Order Difference

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.

scholarly journals Fractional-Order SIR Epidemic Model for Transmission Prediction of COVID-19 Disease

2020 ◽  
Vol 10 (23) ◽  
pp. 8316
Author(s):  
Kamil Kozioł ◽  
Rafał Stanisławski ◽  
Grzegorz Bialic
Keyword(s):  
Fractional Order ◽  
Epidemic Model ◽  
Dynamic Properties ◽  
Sir Model ◽  
Domain Model ◽  
Sir Epidemic Model ◽  
Step Method ◽  
Order Difference ◽  
Sir Epidemic ◽  
The Time Domain

In this paper, the fractional-order generalization of the susceptible-infected-recovered (SIR) epidemic model for predicting the spread of the COVID-19 disease is presented. The time-domain model implementation is based on the fixed-step method using the nabla fractional-order difference defined by Grünwald-Letnikov formula. We study the influence of fractional order values on the dynamic properties of the proposed fractional-order SIR model. In modeling the COVID-19 transmission, the model’s parameters are estimated while using the genetic algorithm. The model prediction results for the spread of COVID-19 in Italy and Spain confirm the usefulness of the introduced methodology.

PARTIAL FRACTIONAL-ORDER DIFFERENCE IN THE EDGE DETECTION

2014 ◽  
pp. 139-157
Author(s):  
Piotr Duch ◽  
Rafał Jachowicz ◽  
Sylwester Błaszczyk ◽  
Maciej Łaski ◽  
Adam Wulkiewicz ◽  
...  
Keyword(s):  
Edge Detection ◽  
Fractional Order ◽  
Order Difference

scholarly journals Linear isomorphic spaces of fractional-order difference operators

2021 ◽  
Vol 60 (1) ◽  
pp. 1155-1164 ◽  
Author(s):  
S.A. Mohiuddine ◽  
Kuldip Raj ◽  
M. Mursaleen ◽  
Abdullah Alotaibi
Keyword(s):  
Fractional Order ◽  
Difference Operators ◽  
Order Difference
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