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Green Functions of the First Boundary-Value Problem for a Fractional Diffusion—Wave Equation in Multidimensional Domains

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  • Arsen Pskhu

    (Institute of Applied Mathematics and Automation, Kabardin-Balkar Scientific Center of Russian Academy of Sciences, 89-A Shortanov Street, 360000 Nalchik, Russia)

Abstract

We construct the Green function of the first boundary-value problem for a diffusion-wave equation with fractional derivative with respect to the time variable. The Green function is sought in terms of a double-layer potential of the equation under consideration. We prove a jump relation and solve an integral equation for an unknown density. Using the Green function, we give a solution of the first boundary-value problem in a multidimensional cylindrical domain. The fractional differentiation is given by the Dzhrbashyan–Nersesyan fractional differentiation operator. In particular, this covers the cases of equations with the Riemann–Liouville and Caputo derivatives.

Suggested Citation

  • Arsen Pskhu, 2020. "Green Functions of the First Boundary-Value Problem for a Fractional Diffusion—Wave Equation in Multidimensional Domains," Mathematics, MDPI, vol. 8(4), pages 1-15, March.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:4:p:464-:d:337104
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    References listed on IDEAS

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    1. Vasily E. Tarasov, 2019. "On History of Mathematical Economics: Application of Fractional Calculus," Mathematics, MDPI, vol. 7(6), pages 1-28, June.
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