Study on chaos of nonlinear suspension system with fractional-order derivative under random excitation

2021 ◽  
Vol 152 ◽  
pp. 111300
Author(s):  
Enli Chen ◽  
Wuce Xing ◽  
Meiqi Wang ◽  
Wenli Ma ◽  
Yujian Chang
Keyword(s):  
Fractional Order ◽  
Random Excitation ◽  
Suspension System ◽  
Order Derivative ◽  
Fractional Order Derivative

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 Feedback control for two-degree-of-freedom vibration system with fractional-order derivative damping

2017 ◽  
Vol 37 (3) ◽  
pp. 554-564
Author(s):  
Canchang Liu ◽  
Chicheng Ma ◽  
Jilei Zhou ◽  
Lu Liu ◽  
Shuchang Yue ◽  
...  
Keyword(s):  
Feedback Control ◽  
Nonlinear Vibration ◽  
Fractional Order ◽  
Suspension System ◽  
Degree Of Freedom ◽  
Vehicle Suspension ◽  
Vibration System ◽  
Fractional Order Derivative ◽  
Vehicle Suspension System ◽  
Two Degree Of Freedom

A two-degree-of-freedom nonlinear vibration system of a quarter vehicle suspension system is studied by using the feedback control method considered the fractional-order derivative damping. The nonlinear dynamic model of two-degree-of-freedom vehicle suspension system is built and linear velocity and displacement controllers are used to control the nonlinear vibration of the vehicle suspension system. A case of the 1:1 internal resonance is considered. The amplitude–frequency response is obtained with the multiscale method. The asymptotic stability conditions of the nonlinear system can be gotten by using the Routh–Hurwitz criterion and the ranges of control parameters are gained in the condition of stable solutions to the system. The simulation results show that the feedback control can effectively reduce the amplitude of primary resonance, weaken or even eliminate the nonlinear vibration characteristics of the suspension system. Fractional orders have an impact on control performance, which should be considered in the control problem. The study will provide a theoretical basis and reference for the optimal design of the vehicle suspension system.

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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