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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2003, Volume 6, Number 2, Pages 197–203
(Mi sjvm187)
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This article is cited in 7 scientific papers (total in 7 papers)
Stochastic solution to partial differential equations of fractional orders
V. V. Uchaikin, V. V. Saenko Ulyanovsk State University
Abstract:
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 $\beta$.
Received: 30.07.2002 Revised: 01.10.2002
Citation:
V. V. Uchaikin, V. V. Saenko, “Stochastic solution to partial differential equations of fractional orders”, Sib. Zh. Vychisl. Mat., 6:2 (2003), 197–203
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https://www.mathnet.ru/eng/sjvm187 https://www.mathnet.ru/eng/sjvm/v6/i2/p197
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Abstract page: | 469 | Full-text PDF : | 190 | References: | 50 |
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