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A Fokker-Planck equation of fractional order with respect to time. (English) Zbl 0761.60071
Summary: By combining the maximum entropy principle with some considerations related to derivatives of fractional order, one is led to suggest a Fokker-Planck equation of fractional order with respect to time, which could be related to dynamical systems subject to fractional Brownian motion. The relation with the process associated with the equation \(\partial p/\partial t=(-1)^{n+1}\partial^{2n} p/\partial x^{2n}\) is exhibited.

60J70 Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
60K35 Interacting random processes; statistical mechanics type models; percolation theory
Full Text: DOI
[1] DOI: 10.1137/1010093 · Zbl 0179.47801 · doi:10.1137/1010093
[2] Levy P., Univ. California Publ. Statist. 1 pp 331– (1953)
[3] Liouville J., J. de l’Ecole Polytechnique 13 pp 71– (1832)
[4] Krylov V. Yu., Sov. Math. Dokl. 1 pp 760– (1960)
[5] DOI: 10.1214/aop/1176995529 · Zbl 0378.60030 · doi:10.1214/aop/1176995529
[6] DOI: 10.1063/1.526520 · Zbl 0562.60087 · doi:10.1063/1.526520
[7] DOI: 10.1063/1.528841 · Zbl 0722.60085 · doi:10.1063/1.528841
[8] DOI: 10.1063/1.528841 · Zbl 0722.60085 · doi:10.1063/1.528841
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