Geodesic
Stochastic solution to partial differential equations of fractional orders
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 6 (2003) no. 2, pp. 197-203 
V. V. Uchaikin; V. V. Saenko. Stochastic solution to partial differential equations of fractional orders. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 6 (2003) no. 2, pp. 197-203. http://geodesic.mathdoc.fr/item/SJVM_2003_6_2_a8/
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2003_6_2_a8/}
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Partial differential equations containing the fractional derivatives $\partial^{\beta}f/\partial t^{\beta}(0<\beta\leq 1)$ and $(-\Delta_m)^{\alpha/2}(0<\alpha<2)$. are considered. These equations generalize the ordinary diffusion equation to an anomalous one and can be solved by $m$-dimensional isotropic random walk with delay. In contrast to the ordinary case, a free path distribution should have a heavy tail of the inverse power type with the exponent $\alpha$, and the delay time distribution should have a similar tail with the exponent $\beta$.

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