Anomalous diffusion associated with nonlinear fractional derivative Fokker-Planck-like equation: Exact time-dependent solutions

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Article discussing research on anomalous diffusion associated with nonlinear fractional derivative Fokker-Planck-like equation.

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6 p.

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Bologna, Mauro; Tsallis, Constantino & Grigolini, Paolo August 2000.

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Article discussing research on anomalous diffusion associated with nonlinear fractional derivative Fokker-Planck-like equation.

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6 p.

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Copyright 2000 American Physical Society. The following article appeared in Physical Review E, 62:2, pp. 2213-2218; http://pre.aps.org/abstract/PRE/v62/i2/p2213_1

Abstract: We consider the d=1 nonlinear Fokker-Planck-like equation with fractional derivatives (∂/∂t)P(x,t) = D(∂ƴ/∂xƴ)[P(x,t]v. Exact time-dependent solutions are found for v = (2 - y)/(1 + y)(-∞ < y ⩽ 2). By considering the long-distance asymptotic behavior of these solutions, a connection is established, namely, q = (y + 3)/(Y + 1)(0 < y ⩽ 2), with the solutions optimizing the nonextensive entropy characterized by index q. Interestingly enough, this relation coincides with the only already known for Lévy-like superdiffusion (i.e., v = 1 and 0 < y ⩽ 2). Finally, for (y,v) = (2,0) the authors obtain q=5/3, which differs from the value q = 2 corresponding to the y = 2 solutions available in the literature (v < 1 porous medium equation), thus exhibiting nonuniform convergence.

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  • Physical Review E, 2000, College Park: American Physical Society, pp. 2213-2218

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  • Publication Title: Physical Review E
  • Volume: 62
  • Issue: 2
  • Page Start: 2213
  • Page End: 2218
  • Pages: 6
  • Peer Reviewed: Yes

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  • August 2000

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  • March 9, 2012, 2:17 p.m.

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  • May 12, 2014, 12:08 p.m.

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Bologna, Mauro; Tsallis, Constantino & Grigolini, Paolo. Anomalous diffusion associated with nonlinear fractional derivative Fokker-Planck-like equation: Exact time-dependent solutions, article, August 2000; [College Park, Maryland]. (digital.library.unt.edu/ark:/67531/metadc77162/: accessed November 18, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT College of Arts and Sciences.