Theoretical and computational perspectives on the eigenvalues of fourth-order fractional Sturm–Liouville problem. Issue 8 (3rd August 2018)

• Record Type: Journal Article
• Authors: Al-Mdallal, Qasem; Al-Refai, Mohammed; Syam, Muhammed; Al-Srihin, Moh'd Khier
• Is Part Of: International journal of computer mathematics. Volume 95:Issue 8(2018)
• Page Start: 1548
• Page End: 1564
• Publication Date: 2018-08-03
• Subjects: Caputo derivative -- fractional Sturm–Liouville problems -- eigenvalues -- fractional series solution; 26A33 -- 34L15 -- 34A08; Computers -- Periodicals; Numerical analysis -- Periodicals; Automation -- Periodicals; 004.0151
• DOI: 10.1080/00207160.2017.1322690
• Languages: English
• ISSNs: 0020-7160

Abstract

ABSTRACT: In this paper, we discuss a class of eigenvalue problems of fractional differential equations of orderα ∈ ( 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 valueα c ∈ ( 3, 4 ] at which the problem has no eigenvalue (forα < α c ), only one eigenvalue (atα = α c ), a finite or infinitely many eigenvalues (forα > α c ). The efficiency and accuracy of the present algorithm are demonstrated through several numerical examples.