TY - JOUR
T1 - Theoretical and computational perspectives on the eigenvalues of fourth-order fractional Sturm–Liouville problem
AU - Al-Mdallal, Qasem
AU - Al-Refai, Mohammed
AU - Syam, Muhammed
AU - Al-Srihin, Moh'd Khier
N1 - Publisher Copyright:
© 2017 Informa UK Limited, trading as Taylor & Francis Group.
PY - 2018/8/3
Y1 - 2018/8/3
N2 - 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.
AB - 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.
KW - Caputo derivative
KW - eigenvalues
KW - fractional Sturm–Liouville problems
KW - fractional series solution
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U2 - 10.1080/00207160.2017.1322690
DO - 10.1080/00207160.2017.1322690
M3 - Article
AN - SCOPUS:85019179361
SN - 0020-7160
VL - 95
SP - 1548
EP - 1564
JO - International Journal of Computer Mathematics
JF - International Journal of Computer Mathematics
IS - 8
ER -