Language:   Search:   Contact
Zentralblatt MATH has released its new interface!
For an improved author identification, see the new author database of ZBMATH.

# Advanced Search

Query:
Fill in the form and click »Search«...
Format:
Display: entries per page entries
Zbl 0973.35012
Gorenflo, Rudolf; Luchko, Yuri; Mainardi, Francesco
Wright functions as scale-invariant solutions of the diffusion-wave equation.
(English)
[J] J. Comput. Appl. Math. 118, No.1-2, 175-191 (2000). ISSN 0377-0427

The authors obtain the time-fractional diffusion-wave equation from the classical diffusion or wave equation by replacing the first- or second-order time derivative by a fractional derivative of order $\alpha$ $(0<\alpha\le 2)$.\par They show by using the similarity method and the method of the Laplace transform that the scale-invariant solutions of the mixed problem of signaling type for time-fractional diffusion-wave equation are given in terms of the Wright function in the case $0<\alpha< 1$ and in terms of the generalized Wright function in the case $1<\alpha< z$.\par The authors give the reduced equation for the scale-invariant solutions in terms of the Caputo-type modification of the Erdélyi-Kober fractional differential operator.
[Ismail Taqi Ali (Safat)]
MSC 2000:
*35A25 Other special methods (PDE)
26A33 Fractional derivatives and integrals (real functions)
33E20 Functions defined by series and integrals
45J05 Integro-ordinary differential equations
45K05 Integro-partial differential equations

Keywords: time-fractional diffusion-wave equation; similarity method; Laplace transform; mixed problem; reduced equation for the scale-invariant solutions; Erdélyi-Kober fractional differential operator

Login Username: Password:

Highlights
Master Server

### Zentralblatt MATH Berlin [Germany]

© FIZ Karlsruhe GmbH

Zentralblatt MATH master server is maintained by the Editorial Office in Berlin, Section Mathematics and Computer Science of FIZ Karlsruhe and is updated daily.

Other Mirror Sites

Copyright © 2013 Zentralblatt MATH | European Mathematical Society | FIZ Karlsruhe | Heidelberg Academy of Sciences
Published by Springer-Verlag | Webmaster