Fractional Laguerre spectral methods and their applications to fractional differential equations on unbounded domain
| Autor: | Tarek Aboelenen, H.M. El-Hawary, Shaaban A. Bakr |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2015 |
| Předmět: |
Petrov‰ÛÒGalerkin spectral methods
Applied Mathematics approximation results Mathematical analysis singular fractional Sturm‰ÛÒLiouville operator 010103 numerical & computational mathematics 01 natural sciences weighted Sobolev spaces Domain (mathematical analysis) Computer Science Applications Fractional calculus 010101 applied mathematics Sobolev space Computational Theory and Mathematics Laguerre polynomials Initial value problem fractional-polynomials eigenfunctions Boundary value problem 0101 mathematics Spectral method Eigenvalues and eigenvectors Mathematics |
| Zdroj: | BIRD: BCAM's Institutional Repository Data instname |
| DOI: | 10.1080/00207160.2015.1119270 |
| Popis: | In this article, we first introduce a singular fractional Sturm-Liouville problem (SFSLP) on unbounded domain. The associated fractional differential operator is both Weyl and Caputo type. The properties of spectral data for fractional operator on unbounded domain have been investigated. Moreover, it has been shown that the eigenvalues of the singular problem are real-valued and the corresponding eigenfunctions are orthogonal. The analytical eigensolutions of SFSLP are obtained and defined as generalized Laguerre fractional-polynomials. The optimal approximation of such generalized Laguerre fractional-polynomials in suitably weighted Sobolev spaces involving fractional derivatives has been derived. We construct an efficient generalized Laguerre fractional-polynomials-Petrov–Galerkin methods for a class of fractional initial value problems and fractional boundary value problems. As a numerical example, we examine space fractional advection–diffusion equation. Our theoretical results are confirmed by associated numerical results. |
| Databáze: | OpenAIRE |
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