Stationary Solutions of the Fractional Kinetic Equation with a~Symmetric Power-Law Potential
Teoretičeskaâ i matematičeskaâ fizika, Tome 131 (2002) no. 1, pp. 162-176
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The properties of stationary solutions of the one-dimensional fractional Einstein–Smoluchowski equation with a potential of the form $x^{2m+2}$, $m=1,2,\dots$, and of the Riesz spatial fractional derivative of order $\alpha$, $1\leq\alpha\leq2$ are studied analytically and numerically. We show that for $1\leq\alpha2$, the stationary distribution functions have power-law asymptotic approximations decreasing as $x^{-(\alpha+2m+1)}$ for large values of the argument. We also show that these distributions are bimodal.
@article{TMF_2002_131_1_a13,
author = {V. Yu. Gonchar and L. V. Tanatarov and A. V. Chechkin},
title = {Stationary {Solutions} of the {Fractional} {Kinetic} {Equation} with {a~Symmetric} {Power-Law} {Potential}},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {162--176},
publisher = {mathdoc},
volume = {131},
number = {1},
year = {2002},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2002_131_1_a13/}
}
TY - JOUR AU - V. Yu. Gonchar AU - L. V. Tanatarov AU - A. V. Chechkin TI - Stationary Solutions of the Fractional Kinetic Equation with a~Symmetric Power-Law Potential JO - Teoretičeskaâ i matematičeskaâ fizika PY - 2002 SP - 162 EP - 176 VL - 131 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_2002_131_1_a13/ LA - ru ID - TMF_2002_131_1_a13 ER -
%0 Journal Article %A V. Yu. Gonchar %A L. V. Tanatarov %A A. V. Chechkin %T Stationary Solutions of the Fractional Kinetic Equation with a~Symmetric Power-Law Potential %J Teoretičeskaâ i matematičeskaâ fizika %D 2002 %P 162-176 %V 131 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/TMF_2002_131_1_a13/ %G ru %F TMF_2002_131_1_a13
V. Yu. Gonchar; L. V. Tanatarov; A. V. Chechkin. Stationary Solutions of the Fractional Kinetic Equation with a~Symmetric Power-Law Potential. Teoretičeskaâ i matematičeskaâ fizika, Tome 131 (2002) no. 1, pp. 162-176. http://geodesic.mathdoc.fr/item/TMF_2002_131_1_a13/