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

14 Citations (Scopus)

Abstract

In this paper, we discuss a class of eigenvalue problems of fractional differential equations of order (Formula presented.) 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 (Formula presented.) at which the problem has no eigenvalue (for (Formula presented.)), only one eigenvalue (at (Formula presented.)), a finite or infinitely many eigenvalues (for (Formula presented.)). The efficiency and accuracy of the present algorithm are demonstrated through several numerical examples.

Original languageEnglish
Pages (from-to)1-17
Number of pages17
JournalInternational Journal of Computer Mathematics
DOIs
Publication statusAccepted/In press - May 12 2017

Keywords

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

ASJC Scopus subject areas

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

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