scholarly journals A Novel Control Method for Integer Orders Chaos Systems via Fractional-Order Derivative

2011 ◽  
Vol 2011 ◽  
pp. 1-8 ◽  
Author(s):  
Ping Zhou ◽  
Fei Kuang
Keyword(s):  
Theoretical Result ◽  
Fractional Order ◽  
Simple Structure ◽  
Control Method ◽  
Order Derivative ◽  
Control Law ◽  
Fractional Order Control ◽  
Fractional Order Derivative ◽  
Chaos Attractor

A fractional-order control method is obtained to stabilize the point in chaos attractor of integer orders chaos systems. The control law has simple structure and is designed easily. Two examples are also given to illustrate the effectiveness of the theoretical result.

Fractional Order LQR for Optimal Robust Control of a Simple Structure

2007 ◽  
Author(s):  
Abdollah Shafieezadeh ◽  
Keri Ryan ◽  
YangQuan Chen
Keyword(s):  
Robust Control ◽  
Control Problem ◽  
Fractional Order ◽  
Simple Structure ◽  
Control Method ◽  
Linear Quadratic Regulator ◽  
Linear Quadratic ◽  
Fractional Damping ◽  
Fractional Order Control

This study combines fractional order control with linear quadratic regulator (LQR) for optimal robust control of a simple civil structure. As a first attempt, the purpose of this paper is to demonstrate that, when fractional damping is introduced, additional benefits can be obtained over the best traditional control method. The control problem of this paper can be used as a simple benchmark example to test new control ideas before applying to more complicated models.

GENERALIZED THEORY OF MAGNETO-THERMO-VISCOELASTIC SPHERICAL CAVITY PROBLEM UNDER FRACTIONAL ORDER DERIVATIVE: STATE SPACE APPROACH

2020 ◽  
Vol 9 (11) ◽  
pp. 9769-9780
Author(s):  
S.G. Khavale ◽  
K.R. Gaikwad
Keyword(s):  
State Space ◽  
Fractional Order ◽  
Order Derivative ◽  
Laplace Inversion ◽  
State Space Approach ◽  
Spherical Region ◽  
Fractional Order Derivative ◽  
Numerical Laplace Inversion ◽  
Mathcad Software ◽  
Space Approach

This paper is dealing the modified Ohm's law with the temperature gradient of generalized theory of magneto-thermo-viscoelastic for a thermally, isotropic and electrically infinite material with a spherical region using fractional order derivative. The general solution obtained from Laplace transform, numerical Laplace inversion and state space approach. The temperature, displacement and stresses are obtained and represented graphically with the help of Mathcad software.

scholarly journals Novel hyperbolic and exponential ansatz methods to the fractional fifth-order Korteweg–de Vries equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Choonkil Park ◽  
R. I. Nuruddeen ◽  
Khalid K. Ali ◽  
Lawal Muhammad ◽  
M. S. Osman ◽  
...  
Keyword(s):  
Fractional Derivative ◽  
Fractional Order ◽  
Mathematical Physics ◽  
Order Derivative ◽  
Conformable Fractional Derivative ◽  
Fractional Order Derivative ◽  
De Vries ◽  
Fifth Order ◽  
2D And 3D

Abstract This paper aims to investigate the class of fifth-order Korteweg–de Vries equations by devising suitable novel hyperbolic and exponential ansatze. The class under consideration is endowed with a time-fractional order derivative defined in the conformable fractional derivative sense. We realize various solitons and solutions of these equations. The fractional behavior of the solutions is studied comprehensively by using 2D and 3D graphs. The results demonstrate that the methods mentioned here are more effective in solving problems in mathematical physics and other branches of science.

scholarly journals Iterative analysis of non-linear Swift-Hohenberg equations under nonsingular fractional order derivative

2021 ◽  
pp. 104080
Author(s):  
Israr Ahmad ◽  
Thabet Abdeljawad ◽  
Ibrahim Mahariq ◽  
Kamal Shah ◽  
Nabil Mlaiki ◽  
...  
Keyword(s):  
Fractional Order ◽  
Order Derivative ◽  
Fractional Order Derivative ◽  
Iterative Analysis ◽  
Non Linear

scholarly journals Multiplicity Result of Positive Solutions for Nonlinear Differential Equation of Fractional Order

2012 ◽  
Vol 2012 ◽  
pp. 1-15
Author(s):  
Yang Liu ◽  
Zhang Weiguo
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Nonlinear Differential Equation ◽  
Positive Solutions ◽  
Fractional Order ◽  
Point Theorem ◽  
Boundary Value ◽  
Order Derivative ◽  
Fractional Order Derivative

We investigate the existence of multiple positive solutions for a class of boundary value problems of nonlinear differential equation with Caputo’s fractional order derivative. The existence results are obtained by means of the Avery-Peterson fixed point theorem. It should be point out that this is the first time that this fixed point theorem is used to deal with the boundary value problem of differential equations with fractional order derivative.

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