Theoretical and computational perspectives on the eigenvalues of fourth-order fractional Sturm–Liouville problem

Qasem Al-Mdallal, Mohammed Al-Refai, Muhammed Syam, Moh'd Khier Al-Srihin

Research output: Contribution to journalArticlepeer-review

20 Citations (Scopus)

Abstract

In this paper, we discuss a class of eigenvalue problems of fractional differential equations of order α ∈ (3, 4] with variable coefficients. The method of solution is based on utilizing the fractional series solution to find theoretical eigenfunctions. Then, the eigenvalues are determined by applying the associated boundary conditions. A notable result, for certain cases, is that the eigenfunctions are characterized in terms of the Mittag-Leffler or semi Mittag-Leffler functions. The present findings demonstrate, for certain cases, the existence of a critical value αc ∈ (3, 4] at which the problem has no eigenvalue (for α < αc), only one eigenvalue (at α=αc), a finite or infinitely many eigenvalues (for α > αc). The efficiency and accuracy of the present algorithm are demonstrated through several numerical examples.

Original languageEnglish
Pages (from-to)1548-1564
Number of pages17
JournalInternational Journal of Computer Mathematics
Volume95
Issue number8
DOIs
Publication statusPublished - Aug 3 2018

Keywords

  • Caputo derivative
  • eigenvalues
  • fractional Sturm–Liouville problems
  • fractional series solution

ASJC Scopus subject areas

  • Computer Science Applications
  • Computational Theory and Mathematics
  • Applied Mathematics

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