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Fractal Fract 2018, 2(1), 1; https://doi.org/10.3390/fractalfract2010001

Fractional Diffusion Models for the Atmosphere of Mars

1
Department of Applied Mathematics to the Information and Communications Technologies, Universidad Politécnica de Madrid, 28040 Madrid, Spain
2
Instituto de Matemática Interdisciplinar, Universidad Complutense de Madrid, 28040 Madrid, Spain
*
Author to whom correspondence should be addressed.
Received: 5 December 2017 / Revised: 23 December 2017 / Accepted: 24 December 2017 / Published: 28 December 2017
(This article belongs to the Special Issue Fractional Dynamics)
Full-Text   |   PDF [258 KB, uploaded 28 December 2017]

Abstract

The dust aerosols floating in the atmosphere of Mars cause an attenuation of the solar radiation traversing the atmosphere that cannot be modeled through the use of classical diffusion processes. However, the definition of a type of fractional diffusion equation offers a more accurate model for this dynamic and the second order moment of this equation allows one to establish a connection between the fractional equation and the Ångstrom law that models the attenuation of the solar radiation. In this work we consider both one and three dimensional wavelength-fractional diffusion equations, and we obtain the analytical solutions and numerical methods using two different approaches of the fractional derivative. View Full-Text
Keywords: fractional calculus; Mittag-Leffler type functions; fractional ordinary and partial differential equations; dust; solar radiation fractional calculus; Mittag-Leffler type functions; fractional ordinary and partial differential equations; dust; solar radiation
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Jiménez, S.; Usero, D.; Vázquez, L.; Velasco, M.P. Fractional Diffusion Models for the Atmosphere of Mars. Fractal Fract 2018, 2, 1.

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