Anomalous diffusion, nonlinear fractional Fokker–Planck equation and solutions

We obtain new exact classes of solutions for the nonlinear fractional Fokker–Planck-like equation ∂ t ρ=∂ x { D( x)∂ μ−1 x ρ ν − F( x) ρ} by considering a diffusion coefficient D= D|x| −θ (θ∈ R and D>0) and a drift force F=−k 1x+ k ̄ γx|x| γ−1 (k 1, k ̄ γ,γ∈ R) . Connection with nonextensive stat...

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Bibliographic Details
Published inPhysica A Vol. 319; pp. 245 - 252
Main Authors Lenzi, E.K., Malacarne, L.C., Mendes, R.S., Pedron, I.T.
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.03.2003
Subjects
Anomalous diffusion
Fokker–Planck equation
Tsallis entropy
Fokker–Planck equation
82.20.Db
Tsallis entropy
05.60.+w
66.10.Cb
Anomalous diffusion
05.40.+j
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Summary:We obtain new exact classes of solutions for the nonlinear fractional Fokker–Planck-like equation ∂ t ρ=∂ x { D( x)∂ μ−1 x ρ ν − F( x) ρ} by considering a diffusion coefficient D= D|x| −θ (θ∈ R and D>0) and a drift force F=−k 1x+ k ̄ γx|x| γ−1 (k 1, k ̄ γ,γ∈ R) . Connection with nonextensive statistical mechanics based on Tsallis entropy is also discussed.
ISSN:0378-4371
1873-2119
DOI:10.1016/S0378-4371(02)01495-4