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Anomalous diffusion, nonlinear fractional Fokker–Planck equation and solutions

Author

Listed:
  • Lenzi, E.K.
  • Malacarne, L.C.
  • Mendes, R.S.
  • Pedron, I.T.

Abstract

We obtain new exact classes of solutions for the nonlinear fractional Fokker–Planck-like equation ∂tρ=∂x{D(x)∂μ−1xρν−F(x)ρ} by considering a diffusion coefficient D=D|x|−θ(θ∈R and D>0) and a drift force F=−k1x+k̄γx|x|γ−1(k1,k̄γ,γ∈R). Connection with nonextensive statistical mechanics based on Tsallis entropy is also discussed.

Suggested Citation

  • Lenzi, E.K. & Malacarne, L.C. & Mendes, R.S. & Pedron, I.T., 2003. "Anomalous diffusion, nonlinear fractional Fokker–Planck equation and solutions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 319(C), pages 245-252.
    • Handle: RePEc:eee:phsmap:v:319:y:2003:i:c:p:245-252
    DOI: 10.1016/S0378-4371(02)01495-4
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    Citations

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    Cited by:

    1. Kalogeropoulos, Nikolaos, 2020. "Toward a relative q-entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    2. Sun, HongGuang & Li, Zhipeng & Zhang, Yong & Chen, Wen, 2017. "Fractional and fractal derivative models for transient anomalous diffusion: Model comparison," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 346-353.
    3. Hashemi, M.S., 2015. "Group analysis and exact solutions of the time fractional Fokker–Planck equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 417(C), pages 141-149.
    4. Richard L. Magin & Ervin K. Lenzi, 2021. "Slices of the Anomalous Phase Cube Depict Regions of Sub- and Super-Diffusion in the Fractional Diffusion Equation," Mathematics, MDPI, vol. 9(13), pages 1-29, June.
    5. Rui, Weiguo & Yang, Xinsong & Chen, Fen, 2022. "Method of variable separation for investigating exact solutions and dynamical properties of the time-fractional Fokker–Planck equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 595(C).

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