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

scholarly journals Multiparameter Fractional Difference Linear Control Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Dorota Mozyrska
Keyword(s):  
Control Systems ◽  
Fractional Order ◽  
Initial Conditions ◽  
Linear Control Systems ◽  
Difference Operators ◽  
Fractional Operators ◽  
Fractional Difference ◽  
Order Difference ◽  
Time Control ◽  
Controllability And Observability

The Riemann-Liouville-, Caputo-, and Grünwald-Letnikov-type fractional order difference operators are discussed and used to state and solve the controllability and observability problems of linear fractional order discrete-time control systems with multiorder and multistep. It is shown that the obtained results do not depend on the type of fractional operators and steps. The comparison of systems is made under the number of steps needed, firstly to achieve a final point, and secondly to distinguish initial conditions for particular operator.

Local controllability of nonlinear discrete-time fractional order systems

2013 ◽  
Vol 61 (1) ◽  
pp. 251-256 ◽  
Author(s):  
D. Mozyrska ◽  
E. Pawłuszewicz
Keyword(s):  
Linear Approximation ◽  
Fractional Order ◽  
Discrete Time ◽  
Local Controllability ◽  
Difference Operators ◽  
Fractional Order Systems ◽  
Discrete Time System ◽  
Controllability Problem ◽  
Time System ◽  
Order Difference

Abstract The Riemann-Liouville, Caputo and Gr¨unwald-Letnikov fractional order difference operators are discussed and used to state and solve the controllability problem of a nonlinear fractional order discrete-time system. It is shown that independently of the type of fractional order difference, such a system is locally controllable in q steps if its linear approximation is globally controllable in q steps

scholarly journals Duality of variable fractional order difference operators and its application in identification

2014 ◽  
Vol 62 (4) ◽  
pp. 809-815 ◽  
Author(s):  
D. Sierociuk ◽  
M. Twardy
Keyword(s):  
System Identification ◽  
Least Squares ◽  
Fractional Order ◽  
Least Squares Estimation ◽  
Difference Operators ◽  
Variable Order ◽  
Fractional Systems ◽  
Order Difference

Abstract The paper presents a number of definitions of variable order difference and discusses duality among some of them. The duality is used to improve the performance of the least squares estimation when applied to variable order difference fractional systems. It turns out, that by appropriate exploitation of duality one can reduce the estimator variance when system identification is carried out.

New fractional order discrete Grüss type inequality

2021 ◽  
Vol 71 (1) ◽  
pp. 33-42
Author(s):  
Serkan Asliyüce ◽  
A. Feza Güvenilir
Keyword(s):  
Fractional Order ◽  
Type Inequality ◽  
Difference Operators

Abstract The aim of this study is to establish new discrete Grüss type inequality using fractional order h-sum and h-difference operators that generalize the fractional sum and difference operators.

scholarly journals Discrete fractional order two-point boundary value problem with some relevant physical applications

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
A. George Maria Selvam ◽  
Jehad Alzabut ◽  
R. Dhineshbabu ◽  
S. Rashid ◽  
M. Rehman
Keyword(s):  
Boundary Value Problem ◽  
Fractional Order ◽  
Contraction Mapping ◽  
Boundary Value ◽  
Contraction Mapping Principle ◽  
Difference Operators ◽  
Point Boundary ◽  
Uniqueness Of Solutions ◽  
Fractional Difference ◽  
Rassias Stability

Abstract The results reported in this paper are concerned with the existence and uniqueness of solutions of discrete fractional order two-point boundary value problem. The results are developed by employing the properties of Caputo and Riemann–Liouville fractional difference operators, the contraction mapping principle and the Brouwer fixed point theorem. Furthermore, the conditions for Hyers–Ulam stability and Hyers–Ulam–Rassias stability of the proposed discrete fractional boundary value problem are established. The applicability of the theoretical findings has been demonstrated with relevant practical examples. The analysis of the considered mathematical models is illustrated by figures and presented in tabular forms. The results are compared and the occurrence of overlapping/non-overlapping has been discussed.

scholarly journals An infinite family of higher-order difference operators that commute with Ruijsenaars operators of type A

2021 ◽  
Vol 111 (4) ◽  
Author(s):  
Masatoshi Noumi ◽  
Ayako Sano
Keyword(s):  
Infinite Family ◽  
Type A ◽  
Higher Order ◽  
Difference Operators ◽  
Order Difference

AbstractWe introduce a new infinite family of higher-order difference operators that commute with the elliptic Ruijsenaars difference operators of type A. These operators are related to Ruijsenaars’ operators through a formula of Wronski type.

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.

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