Stochastic solutions of generalized time-fractional evolution equations

被引：0
作者：
Christian Bender
Yana A. Butko
机构：
[1] Saarland University,Faculty of Mathematics and Computer Science
[2] Technical University of Braunschweig,Institute of Mathematical Stochastics
来源：
Fractional Calculus and Applied Analysis | 2022年 / 25卷
关键词：
Time-fractional evolution equations (primary); Fractional calculus; Randomly scaled Gaussian processes; Randomly scaled Lévy processes; Randomely slowed-down / speeded-up Lévy processes; Linear fractional Lévy motion; Generalized grey Brownian motion; Inverse subordinators; Marichev-Saigo-Maeda operators of fractional calculus; Appell functions; Three parameter Mittag-Leffler function; Feynman-Kac formulae; Anomalous diffusion; 26A33 (primary); 33E12; 34A08; 34K37; 35R11; 60G22;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We consider a general class of integro-differential evolution equations which includes the governing equation of the generalized grey Brownian motion and the time- and space-fractional heat equation. We present a general relation between the parameters of the equation and the distribution of the underlying stochastic processes, as well as discuss different classes of processes providing stochastic solutions of these equations. For a subclass of evolution equations, containing Marichev-Saigo-Maeda time-fractional operators, we determine the parameters of the corresponding processes explicitly. Moreover, we explain how self-similar stochastic solutions with stationary increments can be obtained via linear fractional Lévy motion for suitable pseudo-differential operators in space.
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页码：488 / 519
页数：31
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