Distributed-order space-time fractional diffusions in bounded domains
نویسندگان
چکیده
We consider the distributed-order space-time fractional heat type equation \begin{document}$ \mathbb{D}^{(\nu)}u(t, x) = -(-\Delta)^{\alpha/2}u(t, x), \ t>0, x\in D, $\end{document} where$ \mathbb{D}^{(\nu)} $ is derivative based on Caputo time-fractional derivative, -(-\Delta)^{\alpha/2} generator of an isotropic stable process for \alpha\in(0, 2] $, D a bounded domain in \mathbb{R}^d and \nu finite Borel measure, known as mixing measure. An important application diffusions to model ultraslow where plume particles spreads at logarithmic rate described Sinai (Theory Probab. Appl., 27 (1982) 256–268). Using analytical tools, we provide explicit classical solution stochastic analogue this domains with zero exterior boundary conditions. also show that our results still hold when measure time-derivative singular. Our extend case obtained Naber (Fractals 12(2004) 23–32) Meerschaert et al. (J. Math. Anal. 379(2011) 216–228).
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ژورنال
عنوان ژورنال: Discrete and Continuous Dynamical Systems - Series S
سال: 2023
ISSN: ['1937-1632', '1937-1179']
DOI: https://doi.org/10.3934/dcdss.2023022