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Mathematics > Analysis of PDEs

arXiv:1805.02464 (math)
[Submitted on 7 May 2018 (v1), last revised 31 Aug 2018 (this version, v2)]

Title:Stochastic solutions for space-time fractional evolution equations on bounded domain

Authors:Lorenzo Toniazzi
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Abstract: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 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.
Comments: 34 pages, 1 figure. To appear in J Math Anal Appl
Subjects: Analysis of PDEs (math.AP)
Cite as: arXiv:1805.02464 [math.AP]
  (or arXiv:1805.02464v2 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.1805.02464

Submission history

From: Lorenzo Toniazzi [view email]
[v1] Mon, 7 May 2018 12:06:33 UTC (34 KB)
[v2] Fri, 31 Aug 2018 15:45:33 UTC (38 KB)
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