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Nonlocal Transport Processes and the Fractional Cattaneo-Vernotte Equation
Joint Authors
Aguilar, José Francisco Gómez
Olivares Peregrino, Víctor Hugo
Escobar-Jiménez, R. F.
Córdova-Fraga, T.
Tórres-Jiménez, J.
Guerrero-Ramírez, G. V.
Source
Mathematical Problems in Engineering
Issue
Vol. 2016, Issue 2016 (31 Dec. 2016), pp.1-15, 15 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2016-06-30
Country of Publication
Egypt
No. of Pages
15
Main Subjects
Abstract EN
The Cattaneo-Vernotte equation is a generalization of the heat and particle diffusion equations; this mathematical model combines waves and diffusion with a finite velocity of propagation.
In disordered systems the diffusion can be anomalous.
In these kinds of systems, the mean-square displacement is proportional to a fractional power of time not equal to one.
The anomalous diffusion concept is naturally obtained from diffusion equations using the fractional calculus approach.
In this paper we present an alternative representation of the Cattaneo-Vernotte equation using the fractional calculus approach; the spatial-time derivatives of fractional order are approximated using the Caputo-type derivative in the range ( 0,2 ] .
In this alternative representation we introduce the appropriate fractional dimensional parameters which characterize consistently the existence of the fractional space-time derivatives into the fractional Cattaneo-Vernotte equation.
Finally, consider the Dirichlet conditions, the Fourier method was used to find the full solution of the fractional Cattaneo-Vernotte equation in analytic way, and Caputo and Riesz fractional derivatives are considered.
The advantage of our representation appears according to the comparison between our model and models presented in the literature, which are not acceptable physically due to the dimensional incompatibility of the solutions.
The classical cases are recovered when the fractional derivative exponents are equal to 1 .
American Psychological Association (APA)
Aguilar, José Francisco Gómez& Córdova-Fraga, T.& Tórres-Jiménez, J.& Escobar-Jiménez, R. F.& Olivares Peregrino, Víctor Hugo& Guerrero-Ramírez, G. V.. 2016. Nonlocal Transport Processes and the Fractional Cattaneo-Vernotte Equation. Mathematical Problems in Engineering،Vol. 2016, no. 2016, pp.1-15.
https://search.emarefa.net/detail/BIM-1112610
Modern Language Association (MLA)
Aguilar, José Francisco Gómez…[et al.]. Nonlocal Transport Processes and the Fractional Cattaneo-Vernotte Equation. Mathematical Problems in Engineering No. 2016 (2016), pp.1-15.
https://search.emarefa.net/detail/BIM-1112610
American Medical Association (AMA)
Aguilar, José Francisco Gómez& Córdova-Fraga, T.& Tórres-Jiménez, J.& Escobar-Jiménez, R. F.& Olivares Peregrino, Víctor Hugo& Guerrero-Ramírez, G. V.. Nonlocal Transport Processes and the Fractional Cattaneo-Vernotte Equation. Mathematical Problems in Engineering. 2016. Vol. 2016, no. 2016, pp.1-15.
https://search.emarefa.net/detail/BIM-1112610
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1112610