Nonlocal electrical diffusion equation

作者：Gomez Aguilar J F^*; Escobar Jimemez R F; Olivares Peregrino V H; Benavides Cruz M; Calderon Ramon C

来源：International Journal of Modern Physics C, 2016, 27(1): 1650007.

DOI：10.1142/S0129183116500078

• Fractional diffusion current
• Caputo derivative
• Mittag-Leffler function
• subdiffusion
• superdiffusion

In this paper, we present an analysis and modeling of the electrical diffuusion 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 < beta <= 1 and for the time domain is 0 < gamma <= 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.

• 出版日期2016-1