A Numerical Study of Eigenvalues and Eigenfunctions of Fractional Sturm-Liouville Problems via Laplace Transform

In this paper, we consider a class of fractional Sturm-Liouville problems, in which the second order derivative is replaced by the Caputo fractional derivative. The Laplace transform method is applied to obtain algebraic equations. Then, the eigenvalues and the eigenfunctions of the fractional Sturm...

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Bibliographic Details
Published in:Indian journal of pure and applied mathematics Vol. 51; no. 3; pp. 857 - 868
Main Authors: Sadabad, Mahnaz Kashfi, Akbarfam, Aliasghar Jodayree, Shiri, Babak
Format: Journal Article
Language:English
Published: New Delhi Indian National Science Academy 01.09.2020
Springer Nature B.V
Subjects:
Applications of Mathematics
Eigenvalues
Eigenvectors
Laplace transforms
Mathematics
Mathematics and Statistics
Numerical Analysis
Numerical methods
65N25
35R11
34B24
Laplace transform
Fractional Sturm-Liouville problem
Caputo fractional derivative
ISSN:0019-5588, 0975-7465
Online Access:Get full text
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Summary:In this paper, we consider a class of fractional Sturm-Liouville problems, in which the second order derivative is replaced by the Caputo fractional derivative. The Laplace transform method is applied to obtain algebraic equations. Then, the eigenvalues and the eigenfunctions of the fractional Sturm-Liouville problems are obtained numerically. We provide a convergence analysis for given method. Finally, the simplicity and efficiency of the numerical method is shown by some examples.
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ISSN:0019-5588
0975-7465
DOI:10.1007/s13226-020-0436-2