Fundamental Results of Conformable Sturm-Liouville Eigenvalue Problems
Joint Authors
Abdeljawad (Maraaba), T.
Al-Refai, Mohammed
Source
Issue
Vol. 2017, Issue 2017 (31 Dec. 2017), pp.1-7, 7 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2017-09-14
Country of Publication
Egypt
No. of Pages
7
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Al-Refai, Mohammed& Abdeljawad (Maraaba), T.. 2017. Fundamental Results of Conformable Sturm-Liouville Eigenvalue Problems. Complexity،Vol. 2017, no. 2017, pp.1-7.
https://search.emarefa.net/detail/BIM-1142757
Modern Language Association (MLA)
Al-Refai, Mohammed& Abdeljawad (Maraaba), T.. Fundamental Results of Conformable Sturm-Liouville Eigenvalue Problems. Complexity No. 2017 (2017), pp.1-7.
https://search.emarefa.net/detail/BIM-1142757
American Medical Association (AMA)
Al-Refai, Mohammed& Abdeljawad (Maraaba), T.. Fundamental Results of Conformable Sturm-Liouville Eigenvalue Problems. Complexity. 2017. Vol. 2017, no. 2017, pp.1-7.
https://search.emarefa.net/detail/BIM-1142757
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1142757