Numerical solutions of Fourier's law involving fractional derivatives with bi-order

被引：3

作者：

Gomez-Aguilar, J. F. ^{[1
]}

Atangana, A. ^{[2
]}

Escobar-Jimenez, R. F. ^{[3
]}

机构：

[1] Tecnol Nacl Mexico, CONACyT Ctr Nacl Invest & Desarrollo Tecnol, Interior Internado Palmira S-N, Cuernavaca 62490, Morelos, Mexico

[2] Univ Free State, Fac Nat & Agr Sci, Inst Groundwater Studies, ZA-9300 Bloemfontein, South Africa

[3] Tecnol Nacl Mexico, Ctr Nacl Invest & Desarrollo Tecnol, Interior Internado Palmira S-N, Cuernavaca 62490, Morelos, Mexico

来源：

SCIENTIA IRANICA | 2018年 / 25卷 / 04期

关键词：

Anomalous diffusion; Fractional heat transfer model; Iterative method; Bi-order fractional derivative; Non-Fourier heat conduction; HEAT-CONDUCTION EQUATION; HAVRILIAK-NEGAMI MEDIA; CALCULUS; THERMOELASTICITY; CYLINDER; MODEL;

D O I：

10.24200/sci.2017.4342

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

In this paper, we present an alternative representation of the fractional spacetime Fourier's law equation using the concept of derivative with two fractional orders a and beta. The new definitions are based on the concept of power law and the generalized Mittag-Leffler function, where the first fractional order is incorporated into the power law function, and the second fractional order is the generalized Mittag-Leffler function. The new approach is capable of considering media with two different layers, scales, and properties. The generalization of this equation exhibits different cases of anomalous behaviors and Non-Fourier heat conduction processes. Numerical solutions are obtained using an iterative scheme. (C) 2018 Sharif University of Technology. All rights reserved.

引用

页码：2175 / 2185

页数：11

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