Enhanced FPGA realization of the fractional-order derivative and application to a variable-order chaotic system

The unstable equilibrium points of the fractional-order Lorenz chaotic system can be controlled via fractional-order derivative, and chaos synchronization for the fractional-order Lorenz chaotic system can be achieved via fractional-order derivative. The control and synchronization technique, based on stability theory of fractional-order systems, is simple and theoretically rigorous. The numerical simulations demonstrate the validity and feasibility of the proposed method.

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Numerical analysis of a fractional-order chaotic system based on conformable fractional-order derivative

The European Physical Journal Plus ◽

10.1140/epjp/i2017-11306-3 ◽

2017 ◽

Vol 132 (1) ◽

Cited By ~ 47

Author(s):

Shaobo He ◽

Kehui Sun ◽

Xiaoyong Mei ◽

Bo Yan ◽

Siwei Xu

Keyword(s):

Numerical Analysis ◽

Fractional Order ◽

Chaotic System ◽

Order Derivative ◽

Fractional Order Derivative

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A Non-Integer Variable Order Mathematical Model of Human Immunodeficiency Virus and Malaria Coinfection with Time Delay

Complexity ◽

10.1155/2019/4291017 ◽

2019 ◽

Vol 2019 ◽

pp. 1-13 ◽

Cited By ~ 2

Author(s):

A. A. M. Arafa ◽

M. Khalil ◽

A. Sayed

Keyword(s):

Time Delay ◽

Fractional Order ◽

Order Derivative ◽

Variable Order ◽

Fractional Order Derivative ◽

Proposed Model ◽

Immunodeficiency Virus ◽

Predictor Corrector ◽

Disease Free ◽

Hiv Aids

The purpose of this paper is to propose a variable fractional-order model with a constant time delay of the coinfection of HIV/AIDS and malaria. The proposed model describes the interaction between HIV/AIDS and malaria. This model is presented by using variable fractional-order derivative which is an extension of the constant fractional-order derivative to explain a certain pattern in the development of infection of several patients. The presented model has been solved numerically via the predictor-corrector scheme. The local and global stability conditions of the disease-free equilibrium are investigated. Also, numerical simulations are presented for different variable fractional-order derivatives in Caputo sense.

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

Advances in Mathematics: Scientific Journal ◽

10.37418/amsj.9.11.86 ◽

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.

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

Advances in Difference Equations ◽

10.1186/s13662-020-03087-w ◽

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.

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