Fractional diffusion equation and Green function approach: Exact solutions

E.K. Lenzi, R.S. Mendes, G. Gonçalves, M.K. Lenzi and L.R. da Silva

Physica A: Statistical Mechanics and its Applications, 2006, vol. 360, issue 2, 215-226

Abstract: We investigate the solutions of a fractional diffusion equation with radial symmetry by using the Green function approach and by taking the N-dimensional case into account. In our analysis, a spatial time-dependent diffusion coefficient is considered, i.e., D(r,t)=Dtδ-1r-θ/Γ(α). The presence of external forces F(r)=Krε with ε=-1-θ and F(r)=-kr+Krε is also taken into account. In particular, we discuss the results obtained by employing boundary conditions defined on a finite interval, and afterwards the analysis is extended to a semi-infinite interval. Finally, we also discuss a rich class of diffusive processes that can be obtained from the results presented in this work.

Keywords: Anomalous diffusion; Fractional diffusion equation; Green function; Exact solutions (search for similar items in EconPapers)
Date: 2006
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:360:y:2006:i:2:p:215-226

DOI: 10.1016/j.physa.2005.06.073

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