Title of article
Numerical solutions of Fourier’s law involving fractional derivatives with bi-order
Author/Authors
Gomez-Aguilar ، J.F. CONACyT-Centro Nacional de Investigacion y Desarrollo Tecnologico, Tecnologico Nacional de Mexico , Atangana ، Abdon Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences - University of the Free State , Escobar-Jimenez ، R.F. Centro Nacional de Investigacion y Desarrollo Tecnologico, Tecnologico Nacional de Mexico
From page
2175
To page
2185
Abstract
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 α and β. The new definitions are based on the concept of power law and the generalized Mittag-Leffer function, where the first fractional order is incorporated into the power law function, and the second fractional order is the generalized Mittag-Leffer 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.
Keywords
Anomalous difiusion , Fractional heat transfer model , Iterative Method , Bi , order fractional derivative , Non , Fourier heat conduction
Journal title
Scientia Iranica(Transactions B:Mechanical Engineering)
Journal title
Scientia Iranica(Transactions B:Mechanical Engineering)
Record number
2631259
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