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.

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 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.

Large deviations in linear control systems with nonzero initial conditions

2015 ◽  
Vol 76 (6) ◽  
pp. 957-976 ◽  
Author(s):  
B. T. Polyak ◽  
A. A. Tremba ◽  
M. V. Khlebnikov ◽  
P. S. Shcherbakov ◽  
G. V. Smirnov
Keyword(s):  
Large Deviations ◽  
Control Systems ◽  
Initial Conditions ◽  
Linear Control ◽  
Linear Control Systems

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 Palm Print Edge Extraction Using Fractional Differential Algorithm

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Chunmei Chi ◽  
Feng Gao
Keyword(s):  
Fractional Order ◽  
Edge Extraction ◽  
Fractional Difference ◽  
Traditional Methods ◽  
Order Difference ◽  
Difference Function ◽  
Fractional Differential ◽  
Differential Algorithm ◽  
Palm Print

Algorithm based on fractional difference was used for the edge extraction of thenar palm print image. Based on fractional order difference function which was deduced from classical fractional differential G-L definition, three filter templates were constructed to extract thenar palm print edge. The experiment results showed that this algorithm can reduce noise and detect rich edge details and has higher SNR than traditional methods.

scholarly journals On the Definitions of Nabla Fractional Operators

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Thabet Abdeljawad ◽  
Ferhan M. Atici
Keyword(s):  
Difference Operator ◽  
Difference Operators ◽  
Fractional Operators ◽  
Initial Value ◽  
Fractional Difference ◽  
Power Rule ◽  
The One ◽  
Definition Of ◽  
The Right ◽  
Commutative Property

We show that two recent definitions of discrete nabla fractional sum operators are related. Obtaining such a relation between two operators allows one to prove basic properties of the one operator by using the known properties of the other. We illustrate this idea with proving power rule and commutative property of discrete fractional sum operators. We also introduce and prove summation by parts formulas for the right and left fractional sum and difference operators, where we employ the Riemann-Liouville definition of the fractional difference. We formalize initial value problems for nonlinear fractional difference equations as an application of our findings. An alternative definition for the nabla right fractional difference operator is also introduced.

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.

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 Some New Difference Inequalities and an Application to Discrete-Time Control Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Hong Zhou ◽  
Deqing Huang ◽  
Wu-Sheng Wang ◽  
Jian-Xin Xu
Keyword(s):  
Control Systems ◽  
Nonlinear Function ◽  
Linear Control ◽  
Linear Control Systems ◽  
Nonlinear Perturbations ◽  
Rigorous Analysis ◽  
Composite Function ◽  
Time Control ◽  
Explicit Bounds ◽  
The Stability

Two new nonlinear difference inequalities are considered, where the inequalities consist of multiple iterated sums, and composite function of nonlinear function and unknown function may be involved in each layer. Under several practical assumptions, the inequalities are solved through rigorous analysis, and explicit bounds for the unknown functions are given clearly. Further, the derived results are applied to the stability problem of a class of linear control systems with nonlinear perturbations.

Sign in / Sign up

Export Citation Format

Share Document