Stochastic classical solutions for space-time fractional evolution equations on a bounded domain

被引：7
|
作者：
Toniazzi, Lorenzo [1 ]
机构：
[1] Univ Warwick, Dept Math, Coventry, W Midlands, England
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2019年 / 469卷 / 02期
基金：
英国工程与自然科学研究理事会;
关键词：
Inhomogeneous Caputo evolution equation; Restricted fractional Laplacian; Mittag-Leffler functions; Stable Levy processes; Nonlocal boundary condition; DIFFUSION-EQUATIONS; RANDOM-WALKS; CAUCHY-PROBLEMS; SUBORDINATORS; CALCULUS;
D O I：
10.1016/j.jmaa.2018.09.030
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Space-time fractional evolution equations are a powerful tool to model diffusion displaying space-time heterogeneity. We prove existence, uniqueness and stochastic representation of classical solutions for an extension of Caputo evolution equations featuring time-nonlocal initial conditions. We discuss the interpretation of the new stochastic representation. As part of the proof a new result about inhomogeneous Caputo evolution equations is proven. (C) 2018 Published by Elsevier Inc.
引用
收藏
页码：594 / 622
页数：29
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