Publication
Fundamental Solution of the Multi-Dimensional Time Fractional Telegraph Equation
| dc.contributor.author | Ferreira, Milton | |
| dc.contributor.author | Rodrigues, M. Manuela | |
| dc.contributor.author | Vieira, Nelson | |
| dc.date.accessioned | 2025-06-18T10:21:28Z | |
| dc.date.available | 2025-06-18T10:21:28Z | |
| dc.date.issued | 2017-08-18 | |
| dc.description.abstract | In this paper we study the fundamental solution (FS) of the multidimensional time-fractional telegraph equation where the time-fractional derivatives of orders α ∈]0,1] and β ∈]1,2] are in the Caputo sense. Using the Fourier transform we obtain an integral representation of the FS in the Fourier domain expressed in terms of a multivariate Mittag-Leffler function. The Fourier inversion leads to a double Mellin-Barnes type integral representation and consequently to a H-function of two variables. An explicit series representation of the FS, depending on the parity of the dimension, is also obtained. As an application, we study a telegraph process with Brownian time. Finally, we present some moments of integer order of the FS, and some plots of the FS for some particular values of the dimension and of the fractional parameters α and β. | eng |
| dc.description.sponsorship | The authors were supported by Portuguese funds through the CIDMA - Center for Research and Development in Mathematics and Applications, and the Portuguese Foundation for Science and Technology (“FCT–Funda-¸cˆao para a Ciˆencia e a Tecnologia”), within project UID/MAT/ 0416/2013. N. Vieira is Auxiliar Researcher, under the FCT Researcher Program 2014 (Ref: IF/00271/2014). | |
| dc.identifier.citation | Ferreira, M., Rodrigues, M.M. & Vieira, N. Fundamental Solution of the Multi-Dimensional Time Fractional Telegraph Equation. FCAA 20, 868–894 (2017). https://doi.org/10.1515/fca-2017-0046 | |
| dc.identifier.doi | 10.1515/fca-2017-0046 | |
| dc.identifier.issn | 1311-0454 | |
| dc.identifier.issn | 1314-2224 | |
| dc.identifier.uri | http://hdl.handle.net/10400.8/13320 | |
| dc.language.iso | eng | |
| dc.peerreviewed | yes | |
| dc.publisher | Springer Science and Business Media LLC | |
| dc.relation | UID/MAT/ 0416/2013 | |
| dc.relation | Ref: IF/00271/2014 | |
| dc.relation.hasversion | https://link.springer.com/article/10.1515/fca-2017-0046 | |
| dc.relation.ispartof | Fractional Calculus and Applied Analysis | |
| dc.rights.uri | N/A | |
| dc.subject | time-fractional telegraph equation | |
| dc.subject | fundamental solution | |
| dc.subject | Caputo fractional derivative | |
| dc.subject | multivariate Mittag-Leffler functions | |
| dc.subject | H-function of two variables | |
| dc.subject | double Mellin-Barnes type integrals | |
| dc.title | Fundamental Solution of the Multi-Dimensional Time Fractional Telegraph Equation | eng |
| dc.type | journal article | |
| dspace.entity.type | Publication | |
| oaire.citation.endPage | 894 | |
| oaire.citation.issue | 4 | |
| oaire.citation.startPage | 868 | |
| oaire.citation.title | Fractional Calculus and Applied Analysis: An International Journal for Theory and Applications | |
| oaire.citation.volume | 20 | |
| oaire.version | http://purl.org/coar/version/c_970fb48d4fbd8a85 |