The first boundary-value problem for a fractional diffusion-wave equation in a non-cylindrical domain

2017 ◽  
Vol 81 (6) ◽  
pp. 1212-1233 ◽  
Author(s):  
A. V. Pskhu
Keyword(s):  
Wave Equation ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Fractional Diffusion ◽  
Cylindrical Domain ◽  
Diffusion Wave

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

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 464 ◽  
Author(s):  
Arsen Pskhu
Keyword(s):  
Wave Equation ◽  
Green Function ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Cylindrical Domain ◽  
Fractional Differentiation ◽  
Layer Potential ◽  
Diffusion Wave ◽  
Jump Relation ◽  
The Green Function

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.

scholarly journals Fractional Diffusion–Wave Equation with Application in Electrodynamics

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2086
Author(s):  
Arsen Pskhu ◽  
Sergo Rekhviashvili
Keyword(s):  
Wave Equation ◽  
Boundary Value Problem ◽  
Fractional Derivative ◽  
Initial Conditions ◽  
Sufficient Conditions ◽  
Fractional Diffusion ◽  
Time Variable ◽  
Solution Uniqueness ◽  
Diffusion Wave ◽  
Starting Point

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.

Reconstruction of a time-dependent source term in a time-fractional diffusion-wave equation

2018 ◽  
Vol 27 (11) ◽  
pp. 1577-1594 ◽  
Author(s):  
Xuhong Gong ◽  
Ting Wei
Keyword(s):  
Wave Equation ◽  
Source Term ◽  
Fractional Diffusion ◽  
Time Dependent ◽  
Diffusion Wave
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