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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:469

Article

Toniazzi, Lorenzo¹ 

[1] Univ Warwick, Dept Math, Coventry, W Midlands, England

关键词: Inhomogeneous Caputo evolution equation;    Restricted fractional Laplacian;    Mittag-Leffler functions;    Stable Levy processes;    Nonlocal boundary condition;   

DOI  :  10.1016/j.jmaa.2018.09.030

来源: Elsevier

【 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.

【 授权许可】

Free