Nonlocal electrical diffusion equation

J. F. Gómez-Aguilar (), R. F. Escobar-Jiménez, V. H. Olivares-Peregrino, M. Benavides-Cruz and C. Calderón-Ramón
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J. F. Gómez-Aguilar: Cátedras CONACYT, Centro Nacional de Investigación y Desarrollo Tecnológico, Tecnológico Nacional de México, Interior Internado Palmira, S/N, Col. Palmira C.P. 62490, Cuernavaca, Morelos, México
R. F. Escobar-Jiménez: Centro Nacional de Investigación y Desarrollo Tecnológico, Tecnológico Nacional de México, Interior Internado Palmira S/N, Col. Palmira, C.P. 62490, Cuernavaca, Morelos, México
V. H. Olivares-Peregrino: Centro Nacional de Investigación y Desarrollo Tecnológico, Tecnológico Nacional de México, Interior Internado Palmira S/N, Col. Palmira, C.P. 62490, Cuernavaca, Morelos, México
M. Benavides-Cruz: Facultad de Ingeniería en Electrónica y Comunicaciones, Campus
C. Calderón-Ramón: Facultad de Ingeniería en Electrónica y Comunicaciones, Campus

International Journal of Modern Physics C (IJMPC), 2016, vol. 27, issue 01, 1-12

Abstract: In this paper, we present an analysis and modeling of the electrical diffusion equation using the fractional calculus approach. This alternative representation for the current density is expressed in terms of the Caputo derivatives, the order for the space domain is 0<β≤1 and for the time domain is 0<γ≤2. We present solutions for the full fractional equation involving space and time fractional derivatives using numerical methods based on Fourier variable separation. The case with spatial fractional derivatives leads to Levy flight type phenomena, while the time fractional equation is related to sub- or super diffusion. We show that the mathematical concept of fractional derivatives can be useful to understand the behavior of semiconductors, the design of solar panels, electrochemical phenomena and the description of anomalous complex processes.

Keywords: Fractional diffusion current; Caputo derivative; Mittag–Leffler function; subdiffusion; superdiffusion (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1142/S0129183116500078

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