Numerical methods for the solution of partial difierential equations of fractional order

By Vickie E. Lynch, B. A. Carreras, Diego del-Castillo-Negrete, K. M. Ferreira-mejias, H. R. Hicks. 2003

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A finite element solution for the fractional advection–dispersion equation (2008, methodology): “Besides, some numerical solutions of the FADE only take the left-handed fractional derivative into account [11,23,25,49,50], implying that the backward transition of solute particles that is slower than the average velocity is eliminated.”
Weighted average finite difference methods for fractional diffusion equations (2004, unknown): “The fractional equations in [ 22 ,24,25] are also different from Eq. (1) because the fractional derivatives considered in those papers are spatial derivatives.”
The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics (2004, methodology): “…we employ for determining the PDF defined by the LFFPE are mainly based on the Grünwald–Letnikov representation of the fractional Riesz derivative (Podlubny 1998, Gorenflo 1997, Gorenflo et al 2002a), details of which are also described in Chechkin et al (2003b); see also Lynch et al (2003)20.”
Numerical Approaches to Fractional Integrals and Derivatives: A Review (2020, background): “[78], the integral ∫ xk+1 xk t1−α f (xj − t)dt was evaluated in a more symmetric form.”