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

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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Mathematical and numerical analysis of a three‐species predator‐prey model with herd behavior and time fractional‐order derivative

Mathematical Methods in the Applied Sciences ◽

10.1002/mma.5999 ◽

2019 ◽

Vol 43 (4) ◽

pp. 1736-1752 ◽

Cited By ~ 11

Author(s):

Behzad Ghanbari ◽

Salih Djilali

Keyword(s):

Numerical Analysis ◽

Fractional Order ◽

Order Derivative ◽

Herd Behavior ◽

Predator Prey ◽

Fractional Order Derivative ◽

Predator Prey Model ◽

Prey Model

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

Nonlinear Dynamics ◽

10.1007/s11071-019-05449-w ◽

2020 ◽

Vol 99 (4) ◽

pp. 3143-3154 ◽

Cited By ~ 1

Author(s):

Mohammed F. Tolba ◽

Hani Saleh ◽

Baker Mohammad ◽

Mahmoud Al-Qutayri ◽

Ahmed S. Elwakil ◽

...

Keyword(s):

Fractional Order ◽

Chaotic System ◽

Order Derivative ◽

Variable Order ◽

Fractional Order Derivative

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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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