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

Arsen Pskhu
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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

Mathematics, 2020, vol. 8, issue 4, 1-15

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.

Keywords: diffusion-wave equation; boundary-value problem; green function; double-layer potential; fractional derivative; Dzhrbashyan–Nersesyan operator (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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