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 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.

Existence of Periodic Solutions for a Class of Second-Order Nonlinear Difference Systems

2011 ◽  
Vol 148-149 ◽  
pp. 1164-1169
Author(s):  
Wei Ming Tan ◽  
Fang Su
Keyword(s):  
Critical Point ◽  
Periodic Solutions ◽  
Critical Point Theory ◽  
Point Theory ◽  
Second Order ◽  
Sufficient Condition ◽  
Order Difference ◽  
Difference Systems ◽  
Existence Of Periodic Solutions

In this paper, by using critical point theory, a sufficient condition is obtained on the existence of periodic solutions for a class of nonlinear second-order difference systems.

scholarly journals Probability Transform Based on the Ordered Weighted Averaging and Entropy Difference

2020 ◽  
Vol 15 (4) ◽  
Author(s):  
Lipeng Pan ◽  
Yong Deng
Keyword(s):  
Probability Distribution ◽  
Evidence Theory ◽  
Mass Function ◽  
New Method ◽  
Weighted Averaging ◽  
Minimum Entropy ◽  
Transform Method ◽  
Numerical Examples ◽  
Ordered Weighted Averaging ◽  
Open Issue

Dempster-Shafer evidence theory can handle imprecise and unknown information, which has attracted many people. In most cases, the mass function can be translated into the probability, which is useful to expand the applications of the D-S evidence theory. However, how to reasonably transfer the mass function to the probability distribution is still an open issue. Hence, the paper proposed a new probability transform method based on the ordered weighted averaging and entropy difference. The new method calculates weights by ordered weighted averaging, and adds entropy difference as one of the measurement indicators. Then achieved the transformation of the minimum entropy difference by adjusting the parameter r of the weight function. Finally, some numerical examples are given to prove that new method is more reasonable and effective.

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 Approximate Solutions of the Generalized Abel’s Integral Equations Using the Extension Khan’s Homotopy Analysis Transformation Method

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Mohamed S. Mohamed ◽  
Khaled A. Gepreel ◽  
Faisal A. Al-Malki ◽  
Maha Al-Humyani
Keyword(s):  
Exact Solutions ◽  
Integral Equations ◽  
Method Comparison ◽  
Approximate Solutions ◽  
Transformation Method ◽  
Theory Of Elasticity ◽  
Transform Method ◽  
Numerical Examples ◽  
Homotopy Analysis ◽  
User Friendly

User friendly algorithm based on the optimal homotopy analysis transform method (OHATM) is proposed to find the approximate solutions to generalized Abel’s integral equations. The classical theory of elasticity of material is modeled by the system of Abel integral equations. It is observed that the approximate solutions converge rapidly to the exact solutions. Illustrative numerical examples are given to demonstrate the efficiency and simplicity of the proposed method. Finally, several numerical examples are given to illustrate the accuracy and stability of this method. Comparison of the approximate solution with the exact solutions shows that the proposed method is very efficient and computationally attractive. We can use this method for solving more complicated integral equations in mathematical physical.

scholarly journals A Note on Double Conformable Laplace Transform Method and Singular One Dimensional Conformable Pseudohyperbolic Equations

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 949 ◽  
Author(s):  
Hassan Eltayeb ◽  
Said Mesloub ◽  
Yahya T. Abdalla ◽  
Adem Kılıçman
Keyword(s):  
Present Method ◽  
Decomposition Method ◽  
Numerical Solutions ◽  
High Accuracy ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Numerical Examples ◽  
One Dimensional ◽  
Linear And Nonlinear ◽  
Laplace Decomposition Method

The purpose of this article is to obtain the exact and approximate numerical solutions of linear and nonlinear singular conformable pseudohyperbolic equations and conformable coupled pseudohyperbolic equations through the conformable double Laplace decomposition method. Further, the numerical examples were provided in order to demonstrate the efficiency, high accuracy, and the simplicity of present method.

Intrinsic Fourier Mode Functions

2017 ◽  
Vol 09 (02) ◽  
pp. 1750003
Author(s):  
Vesselin Vatchev
Keyword(s):  
Instantaneous Frequency ◽  
Sufficient Condition ◽  
Fourier Mode ◽  
Intrinsic Mode Functions ◽  
Numerical Examples ◽  
Class Of Functions

In this paper, we study a class of functions that exhibit properties expected from intrinsic mode functions. A type of an empirical instantaneous frequency, depending on the extrema scale, is introduced and its proximity to the classical analytic instantaneous frequency is discussed. We also obtain a sufficient condition for positiveness of the instantaneous frequency and introduce a method similar in nature to EMD but with an empirical frequency as guide in lieu of empirical envelopes. The method is illustrated in several numerical examples.

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