Fundamental results of conformable Sturm-Liouville eigenvalue problems
type: Item
instance of: scholarly article
title: Fundamental results of conformable Sturm-Liouville eigenvalue problems
zbMATH Open document ID: 1373.34046
DOI: 10.1155/2017/3720471
author: Mohammed Al-Refai
author: Thabet Abdeljawad
published in: Complexity
publication date: 2017-10-26T00:00:00Z
review text: Summary: We suggest a regular fractional generalization of the well-known Sturm-Liouville eigenvalue problems. The suggested model consists of a fractional generalization of the Sturm-Liouville operator using conformable derivative and with natural boundary conditions on bounded domains. We establish fundamental results of the suggested model. We prove that the eigenvalues are real and simple and the eigenfunctions corresponding to distinct eigenvalues are orthogonal and we establish a fractional Rayleigh quotient result that can be used to estimate the first eigenvalue. Despite the fact that the properties of the fractional Sturm-Liouville problem with conformable derivative are very similar to the ones with the classical derivative, we find that the fractional problem does not display an infinite number of eigenfunctions for arbitrary boundary conditions. This interesting result will lead to studying the problem of completeness of eigenfunctions for fractional systems.
Mathematics Subject Classification ID: 34B24
zbMATH DE Number: 6798458
zbMATH Keywords: Sturm-Liouville eigenvalue problem
zbMATH Keywords: regular fractional generalization
zbMATH Keywords: fractional Rayleigh quotient
zbMATH Keywords: completeness of eigenfunctions
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2017/3720471
OpenAlex ID: W2754379126
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description: scientific article; zbMATH DE number 6798458