TY - JOUR
T1 - On fractional-Legendre spectral Galerkin method for fractional Sturm–Liouville problems
AU - Al-Mdallal, Qasem M.
N1 - Funding Information:
Authors would like to acknowledge and express their gratitude to the United Arab Emirates University, Al Ain, UAE for providing the financial support with Grant No. 31S240-UPAR (2) 2016.
Publisher Copyright:
© 2018 Elsevier Ltd
PY - 2018/11
Y1 - 2018/11
N2 - In this paper, we present a numerical technique for solving fractional Sturm–Liouville problems with variable coefficients subject to mixed boundary conditions. The proposed algorithm is a spectral Galerkin method based on fractional-order Legendre functions. Tedious manipulation of the series appearing in the implementation of the method have been carried out to obtain a system of algebraic equations for the coefficients. Our findings demonstrate the possibility of having no eigenvalues, finite number of eigenvalues or infinite number of eigenvalues depending on the fractional order. The convergence and effectiveness of the present algorithm are demonstrated through several numerical examples.
AB - In this paper, we present a numerical technique for solving fractional Sturm–Liouville problems with variable coefficients subject to mixed boundary conditions. The proposed algorithm is a spectral Galerkin method based on fractional-order Legendre functions. Tedious manipulation of the series appearing in the implementation of the method have been carried out to obtain a system of algebraic equations for the coefficients. Our findings demonstrate the possibility of having no eigenvalues, finite number of eigenvalues or infinite number of eigenvalues depending on the fractional order. The convergence and effectiveness of the present algorithm are demonstrated through several numerical examples.
KW - Caputo derivative
KW - Eigenvalues and eigenfunctions
KW - Fractional Legendre functions
KW - Fractional Sturm–Liouville problems
KW - Spectral methods
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U2 - 10.1016/j.chaos.2018.09.032
DO - 10.1016/j.chaos.2018.09.032
M3 - Article
AN - SCOPUS:85054082488
SN - 0960-0779
VL - 116
SP - 261
EP - 267
JO - Chaos, Solitons and Fractals
JF - Chaos, Solitons and Fractals
ER -