Analysis of the Drude model in view of the conformable derivative

Rosales, J. J.; Godínez, F. A.; Banda, V.; Valencia, G.H.

doi:10.1016/j.ijleo.2018.10.079

Cited by 20 publications

(17 citation statements)

References 23 publications

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“…Additionally, the computing burden when using this operator is considerably lighter than when using other fractional derivative definitions. All these features have been corroborated in the literature, where there have been a large number of works carried out with this definition [16][17][18][19][20][21][22].…”

Section: Introductionsupporting

confidence: 53%

Entropy Generation in a Mass-Spring-Damper System Using a Conformable Model

2020

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This article studies the entropy generation of a mass-spring-damper mechanical system, under the conformable fractional operator definition. We perform several simulations by varying the fractional order γ and the damping ratio ζ , including the usual dynamic response when γ = 1.0 and the typical damping cases. We analyze the entropy production for this system and its strong dependency on both γ and ζ parameters. Therefore, we determine their optimal values to obtain the highest efficiency of the MSD response, as well as other impressive features.

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Section: Introductionsupporting

confidence: 53%

Entropy Generation in a Mass-Spring-Damper System Using a Conformable Model

2020

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“…For the homogeneous KdV equation when = 1, we compare our work with exact solution of the KdV equation which is brought in (13) and results are given in t = 0.01 and Ω = [−2.5,2.5] as follows in Table 1 and Figure 1. We also show the solution of the homogeneous KdV equation in time interval [0, 1] in Figure 2.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…Khalil et al [8] introduced a definition for the derivative which is satisfied most properties of classical derivative despite the other definition of the fractional derivative. Its applications can be referred to the quantum mechanics and the fluid dynamics [9][10][11][12][13][14]. Bertrand duopoly game to that based on conformable derivative was developed by Xin et al [15].…”

mentioning

confidence: 99%

Numerical solutions of the initial boundary value problem for the perturbed conformable time Korteweg‐de Vries equation by using the finite element method

Pedram

Rostamy

2020

Numerical Methods Partial

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In this paper, we investigate the initial‐boundary‐value problem for the nonhomogeneous Korteweg‐de Vries equation with conformable derivative on time part of it. We use the finite element method with B‐spline as the basis functions for obtaining the numerical solutions for this nonlinear equation. In addition, we prove a posteriori and a priori errors for it. These show the adaptivity and convergence of our method. Also, a posteriori error estimate concludes that the error estimate decreases as α increases. We show the accuracy of our work by comparing with the exact solution for the homogeneous KdV equation. We also bring an example for the nonhomogeneous conformable time KdV equation to demonstrate the accuracy and efficiency of the proposed method. Also, these numerical results are consistent with the result of theorems. The numerical results are given in tables and figures.

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“…Over the past few decades, a simple definition called conformable fractional derivative was proposed in [9]. For more results about conformable fractional derivative, we refer the reader to [10][11][12][13][14][15][16][17][18]. This derivative seems to be more natural, and it coincides with the classical definition of the first derivative.…”

Section: Introductionmentioning

confidence: 92%