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On the Non-Local Boundary Value Problem from the Probabilistic Viewpoint

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  • Mirko D’Ovidio

    (Department of Basic and Applied Sciences for Engineering, Sapienza University of Rome, Via A. Scarpa 10, 00161 Rome, Italy)

Abstract

We provide a short introduction of new and well-known facts relating non-local operators and irregular domains. Cauchy problems and boundary value problems are considered in case non-local operators are involved. Such problems lead to anomalous behavior on the bulk and on the surface of a given domain, respectively. Such a behavior should be considered (in a macroscopic viewpoint) in order to describe regular motion on irregular domains (in the microscopic viewpoint).

Suggested Citation

  • Mirko D’Ovidio, 2022. "On the Non-Local Boundary Value Problem from the Probabilistic Viewpoint," Mathematics, MDPI, vol. 10(21), pages 1-26, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:21:p:4122-:d:963742
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    References listed on IDEAS

    as
    1. Chen, Zhen-Qing, 2017. "Time fractional equations and probabilistic representation," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 168-174.
    2. Meerschaert, Mark M. & Scheffler, Hans-Peter, 2008. "Triangular array limits for continuous time random walks," Stochastic Processes and their Applications, Elsevier, vol. 118(9), pages 1606-1633, September.
    3. S. K. Ntouyas & P. Ch. Tsamatos, 1997. "Initial and boundary value problems for partial functional differential equations," International Journal of Stochastic Analysis, Hindawi, vol. 10, pages 1-12, January.
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