Gomez-Aguilar, J., Atangana, A., Escobar-Jimenez, R. (2018). Numerical solutions of Fourier's law involving fractional derivatives with bi-order. Scientia Iranica, 25(4), 2175-2185. doi: 10.24200/sci.2017.4342
J.F. Gomez-Aguilar; Abdon Atangana; R.F. Escobar-Jimenez. "Numerical solutions of Fourier's law involving fractional derivatives with bi-order". Scientia Iranica, 25, 4, 2018, 2175-2185. doi: 10.24200/sci.2017.4342
Gomez-Aguilar, J., Atangana, A., Escobar-Jimenez, R. (2018). 'Numerical solutions of Fourier's law involving fractional derivatives with bi-order', Scientia Iranica, 25(4), pp. 2175-2185. doi: 10.24200/sci.2017.4342
Gomez-Aguilar, J., Atangana, A., Escobar-Jimenez, R. Numerical solutions of Fourier's law involving fractional derivatives with bi-order. Scientia Iranica, 2018; 25(4): 2175-2185. doi: 10.24200/sci.2017.4342
Numerical solutions of Fourier's law involving fractional derivatives with bi-order
1CONACyT-Centro Nacional de Investigacion y Desarrollo Tecnologico. Tecnologico Nacional de Mexico
2Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences. University of the Free State, Bloemfontein 9300, South Africa.
3Centro Nacional de Investigacion y Desarrollo Tecnologico.Tecnologico Nacional de Mexico
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 and . The new de nitions are based on the concept of power law and the generalized Mittag-Leer function, where, the rst fractional order is included in the power law function and the second fractional order is the generalized Mittag-Leer function. The new approach is capable of considering media with two di erent layers, scales and properties. The generalization of this equation exhibit di erent cases of anomalous behavior and Non-Fourier heat conduction processes. Numerical solutions using an iterative scheme were obtained.
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