A numerical approximation for generalized fractional Sturm–Liouville problem with application

Eti Goel, Rajesh K. Pandey, S. Yadav and Om P. Agrawal

Mathematics and Computers in Simulation (MATCOM), 2023, vol. 207, issue C, 417-436

Abstract: In this paper, we present a numerical scheme for the generalized fractional Sturm–Liouville problem (GFSLP) with mixed boundary conditions. The GFSLP is defined in terms of the B-operator consisting of an integral operator with a kernel and a differential operator. One of the main features of the B-operator is that for different kernels, it leads to different Sturm–Liouville Problems (SLPs), and thus the same formulation can be used to discuss different SLPs. We prove the well-posedness of the proposed GFSLP. Further, the approximated eigenvalues of the GFSLP are obtained for two different kernels namely a modified power kernel and the Prabhakar kernel in the B-operator. We obtain real eigenvalues and corresponding orthogonal eigenfunctions. Theoretical and numerical convergence orders of eigenvalues and eigenvectors are also discussed. Further, the numerically obtained eigenvalues and eigenfunctions are used to construct an approximate solution of the one-dimensional fractional diffusion equation defined in a bounded domain.

Keywords: Generalized fractional Sturm–Liouville problem; Numerical approximation; B- operator; Mittag-Leffler kernel (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378475423000034
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:207:y:2023:i:c:p:417-436

DOI: 10.1016/j.matcom.2023.01.003

Access Statistics for this article

Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens

More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier
Bibliographic data for series maintained by Catherine Liu ().