scholarly journals Analysis of Atangana–Baleanu fractional-order SEAIR epidemic model with optimal control

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Chernet Tuge Deressa ◽  
Gemechis File Duressa
Keyword(s):  
Numerical Simulation ◽  
Optimal Control ◽  
Fractional Order ◽  
Control Strategy ◽  
Epidemic Model ◽  
Numerical Scheme ◽  
Order Derivative ◽  
Control Analysis ◽  
Fractional Order Derivative ◽  
Fractional Orders

AbstractWe consider a SEAIR epidemic model with Atangana–Baleanu fractional-order derivative. We approximate the solution of the model using the numerical scheme developed by Toufic and Atangana. The numerical simulation corresponding to several fractional orders shows that, as the fractional order reduces from 1, the spread of the endemic grows slower. Optimal control analysis and simulation show that the control strategy designed is operative in reducing the number of cases in different compartments. Moreover, simulating the optimal profile revealed that reducing the fractional-order from 1 leads to the need for quick starting of the application of the designed control strategy at the maximum possible level and maintaining it for the majority of the period of the pandemic.

scholarly journals Threshold for Chaos of a Duffing Oscillator with Fractional-Order Derivative

2019 ◽  
Vol 2019 ◽  
pp. 1-16 ◽  
Author(s):  
Wuce Xing ◽  
Enli Chen ◽  
Yujian Chang ◽  
Meiqi Wang
Keyword(s):  
Numerical Simulation ◽  
Fractional Order ◽  
Chaotic Motion ◽  
Duffing Oscillator ◽  
Threshold Value ◽  
Order Derivative ◽  
Necessary Condition ◽  
Threshold Curve ◽  
Fractional Order Derivative ◽  
Simulation Results

In this paper, the necessary condition for the chaotic motion of a Duffing oscillator with the fractional-order derivative under harmonic excitation is investigated. The necessary condition for the chaos in the sense of Smale horseshoes is established based on the Melnikov method, and then the chaotic threshold curve is obtained. The largest Lyapunov exponents are provided, and some other typical numerical simulation results, including the time histories, frequency spectrograms, phase portraits, and Poincare maps, are presented and compared. From the analysis of the numerical simulation results, it could be found that, near the chaotic threshold curve, the system generates chaos via the period-doubling bifurcation, from single periodic motion to period-2 motion and period-4 motion to chaotic motion. The effects of fractional-order parameters, the stiffness coefficient, and the damping coefficient on the threshold value of the chaotic motion are analytically discussed. The results show that the coefficient of the fractional-order derivative has great effect on the threshold value of the chaotic motion, while the order of the fractional-order derivative has less. The analysis results reveal some new phenomena, and it could be useful for designing or controlling dynamic systems with the fractional-order derivative.

scholarly journals Novel Approaches for Getting the Solution of the Fractional Black–Scholes Equation Described by Mittag-Leffler Fractional Derivative

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Ndolane Sene ◽  
Babacar Sène ◽  
Seydou Nourou Ndiaye ◽  
Awa Traoré
Keyword(s):  
Analytical Solution ◽  
Fractional Derivative ◽  
Fractional Order ◽  
Numerical Scheme ◽  
Fractional Derivatives ◽  
Fractional Integration ◽  
Order Derivative ◽  
Graphical Representations ◽  
Fractional Order Derivative ◽  
Black Scholes

The value of an option plays an important role in finance. In this paper, we use the Black–Scholes equation, which is described by the nonsingular fractional-order derivative, to determine the value of an option. We propose both a numerical scheme and an analytical solution. Recent studies in fractional calculus have included new fractional derivatives with exponential kernels and Mittag-Leffler kernels. These derivatives have been found to be applicable in many real-world problems. As fractional derivatives without nonsingular kernels, we use a Caputo–Fabrizio fractional derivative and a Mittag-Leffler fractional derivative. Furthermore, we use the Adams–Bashforth numerical scheme and fractional integration to obtain the numerical scheme and the analytical solution, and we provide graphical representations to illustrate these methods. The graphical representations prove that the Adams–Bashforth approach is helpful in getting the approximate solution for the fractional Black–Scholes equation. Finally, we investigate the volatility of the proposed model and discuss the use of the model in finance. We mainly notice in our results that the fractional-order derivative plays a regulator role in the diffusion process of the Black–Scholes equation.

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
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