Mathematical Analysis of a Cauchy Problem for the Time-Fractional Diffusion-Wave Equation with [Formula omitted]

This paper deals with a theoretical mathematical analysis of a Cauchy problem for the time-fractional diffusion-wave equation in the upper half-plane, [Formula omitted], [Formula omitted], where the Caputo fractional derivative of order [Formula omitted] is considered. An explicit solution to this C...

Full description

Saved in:
Bibliographic Details
Published in:The Journal of fourier analysis and applications 2018-04, Vol.24 (2), p.560
Main Authors: Goos, Demian Nahuel, Reyero, Gabriela Fernanda
Format: Article
Language:English
Subjects:
Analysis
Numerical analysis
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:This paper deals with a theoretical mathematical analysis of a Cauchy problem for the time-fractional diffusion-wave equation in the upper half-plane, [Formula omitted], [Formula omitted], where the Caputo fractional derivative of order [Formula omitted] is considered. An explicit solution to this Cauchy problem is obtained via separation of variables. A first proof of the validity of the obtained results is provided for a certain kind of initial conditions. Throughout this work a new expression of the solution to this problem and its utility for carrying out rigurous proofs are presented. Finally, several new properties of the solution are obtained.
ISSN:1069-5869
DOI:10.1007/s00041-017-9527-9