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Stochastic classical solutions for space-time fractional evolution equations on a bounded domain. (English) Zbl 1401.60126

Summary: 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.

MSC:

60H15 Stochastic partial differential equations (aspects of stochastic analysis)
35R11 Fractional partial differential equations
35R60 PDEs with randomness, stochastic partial differential equations
60J60 Diffusion processes
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