Mathematical Analysis of a Cauchy Problem for the Time-Fractional Diffusion-Wave Equation with α∈0,2

This paper deals with a theoretical mathematical analysis of a Cauchy problem for the time-fractional diffusion-wave equation in the upper half-plane, x ∈ R , t ∈ R + , where the Caputo fractional derivative of order α ∈ 0 , 2 is considered. An explicit solution to this Cauchy problem is obtained vi...

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Bibliographic Details
Published in:The Journal of fourier analysis and applications 2018, Vol.24 (2), p.560-582
Main Authors: Goos, Demian Nahuel, Reyero, Gabriela Fernanda
Format: Article
Language:English
Subjects:
Abstract Harmonic Analysis
Approximations and Expansions
Cauchy problems
Fourier Analysis
Initial conditions
Mathematical analysis
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Partial Differential Equations
Signal,Image and Speech Processing
Wave equations
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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, x ∈ R , t ∈ R + , where the Caputo fractional derivative of order α ∈ 0 , 2 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
1531-5851
DOI:10.1007/s00041-017-9527-9