Mathematical analysis of a Cauchy problem for the time-fractional diffusion-wave equation with \( \alpha \in (0,2) \)
type: Item
instance of: scholarly article
title: Mathematical analysis of a Cauchy problem for the time-fractional diffusion-wave equation with \( \alpha \in (0,2) \)
zbMATH Open document ID: 1394.35553
author: D. Goos
author: G. Reyero
published in: The Journal of Fourier Analysis and Applications
publication date: 2018-04-25T00:00:00Z
review text: Using the properties of the Mittag-Leffler and the Mainardi functions together with the method of separation of variables, the authors obtain new expression for the solutions of a Cauchy problem of the time-fractional diffusion-wave equation in the upper half-plane, \(x\in \mathbb {R}\), \(t\in \mathbb {R}^+\), where the Caputo fractional derivative of order \(\alpha \in (0,2) \) is considered. Several new properties of the solution, using the stated expression, are presented.
reviewed by: Abdallah Bradji
Mathematics Subject Classification ID: 35R11
Mathematics Subject Classification ID: 33E12
Mathematics Subject Classification ID: 35G10
Mathematics Subject Classification ID: 42A38
zbMATH DE Number: 6864556
zbMATH Keywords: time-fractional diffusion-wave equation
zbMATH Keywords: Caputo fractional derivative
zbMATH Keywords: Cauchy problem
zbMATH Keywords: Mittag-Leffler function
zbMATH Keywords: Mainardi function
zbMATH Keywords: Fourier transform
MaRDI profile type: Publication
full work available at URL: s00041-017-9527-9
OpenAlex ID: W2605856890
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DOI: 10.1007/S00041-017-9527-9
description: scientific article; zbMATH DE number 6864556