Please use this identifier to cite or link to this item:
Title: A fractional analysis in higher dimensions for the Sturm-Liouville problem
Author: Ferreira, M.
Rodrigues, M. M.
Vieira, N.
Keywords: Fractional derivatives
Fractional Sturm-Liouville problem
Fractional variational calculus
Eigenvalue problem
Fractional Clifford analysis
Issue Date: Apr-2021
Publisher: De Gruyter
Abstract: In this work, we consider the n-dimensional fractional Sturm-Liouville eigenvalue problem, by using fractional versions of the gradient operator involving left and right Riemann-Liouville fractional derivatives. We study the main properties of the eigenfunctions and the eigenvalues of the associated fractional boundary problem. More precisely, we show that the eigenfunctions are orthogonal and the eigenvalues are real and simple. Moreover, using techniques from fractional variational calculus, we prove in the main result that the eigenvalues are separated and form an infinite sequence, where the eigenvalues can be ordered according to increasing magnitude. Finally, a connection with Clifford analysis is established.
Peer review: yes
DOI: 10.1515/fca-2021-0026
ISSN: 1311-0454
Publisher Version:
Appears in Collections:CIDMA - Artigos
DMat - Artigos
CHAG - Artigos

Files in This Item:
File Description SizeFormat 
artigo32.pdfMFMRNV_FCAA_2021470.36 kBAdobe PDFView/Open

Formato BibTex MendeleyEndnote Degois 

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