Please use this identifier to cite or link to this item:
Title: Application of the fractional Sturm–Liouville theory to a fractional Sturm–Liouville telegraph equation
Author: Ferreira, M.
Rodrigues, M. M.
Vieira, N.
Keywords: Caputo fractional derivatives
Riemann-Liouville fractional derivatives
Fractional Sturm-Liouville operator
Time-space-fractional telegraph equation
Mittag-Leffler functions
Wright functions
Issue Date: Jul-2021
Publisher: Springer
Abstract: In this paper, we consider a non-homogeneous time-space-fractional telegraph equation in $n$-dimensions, which is obtained from the standard telegraph equation by replacing the first- and second-order time derivatives by Caputo fractional derivatives of corresponding fractional orders, and the Laplacian operator by a fractional Sturm-Liouville operator defined in terms of right and left fractional Riemann-Liouville derivatives. Using the method of separation of variables, we derive series representations of the solution in terms of Wright functions, for the homogeneous and non-homogeneous cases. The convergence of the series solutions is studied by using well known properties of the Wright function. We show also that our series can be written using the bivariate Mittag-Leffler function. In the end of the paper some illustrative examples are presented.
Peer review: yes
DOI: 10.1007/s11785-021-01125-3
ISSN: 1661-8254
Appears in Collections:CIDMA - Artigos
DMat - Artigos
FAAG - Artigos

Files in This Item:
File Description SizeFormat 
artigo58.pdfMFMRNV_Sturm-Liouville_CAOT515.88 kBAdobe PDFView/Open

Formato BibTex MendeleyEndnote Degois 

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.