Fractional Diffusion–Wave Equation with Application in Electrodynamics

Arsen Pskhu and Sergo Rekhviashvili
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Arsen Pskhu: Institute of Applied Mathematics and Automation, Kabardino-Balkarian Scientific Center of Russian Academy of Sciences, 89-A Shortanov Street, 360000 Nalchik, Russia
Sergo Rekhviashvili: Institute of Applied Mathematics and Automation, Kabardino-Balkarian Scientific Center of Russian Academy of Sciences, 89-A Shortanov Street, 360000 Nalchik, Russia

Mathematics, 2020, vol. 8, issue 11, 1-13

Abstract: We consider a diffusion–wave equation with fractional derivative with respect to the time variable, defined on infinite interval, and with the starting point at minus infinity. For this equation, we solve an asympotic boundary value problem without initial conditions, construct a representation of its solution, find out sufficient conditions providing solvability and solution uniqueness, and give some applications in fractional electrodynamics.

Keywords: diffusion–wave equation; fundamental solution; fractional derivative on infinite interval; asympotic boundary value problem; problem without initial conditions; Gerasimov–Caputo fractional derivative; Kirchhoff formula; retarded potential (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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