%0 Journal Article
%T Numerical solutions of Fourier's law involving fractional derivatives with bi-order
%J Scientia Iranica
%I Sharif University of Technology
%Z 1026-3098
%A Gomez-Aguilar, J.F.
%A Atangana, Abdon
%A Escobar-Jimenez, R.F.
%D 2018
%\ 08/01/2018
%V 25
%N 4
%P 2175-2185
%! Numerical solutions of Fourier's law involving fractional derivatives with bi-order
%K Anomalous difiusion
%K Fractional heat transfer model
%K Iterative Method
%K Bi-order fractional derivative
%K Non-Fourier heat conduction
%R 10.24200/sci.2017.4342
%X In this paper, we present an alternative representation of the fractional spacetimeFourier's law equation using the concept of derivative with two fractionalorders and . The new denitions are based on the concept of power lawand the generalized Mittag-Leer function, where, the rst fractional orderis included in the power law function and the second fractional order is thegeneralized Mittag-Leer function. The new approach is capable of consideringmedia with two dierent layers, scales and properties. The generalization ofthis equation exhibit dierent cases of anomalous behavior and Non-Fourierheat conduction processes. Numerical solutions using an iterative scheme wereobtained.
%U https://scientiairanica.sharif.edu/article_4342_ccf9a42f1fe362172f8da42497a61daa.pdf