A Chebyshev spectral method for solving Riemann–Liouville fractional boundary value problems

A Chebyshev spectral method for solving Riemann–Liouville fractional boundary value problems

The authors derive a series of explicit formulas to approximate the Riemann–Liouville derivative and integral of arbitrary order by shifted Chebyshev polynomials. This is then applied to solve boundary value problems involving Riemann–Liouville derivatives.

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Veröffentlicht in:Applied mathematics and computation 2014-08, Vol.241, p.140-150
Hauptverfasser: Graef, John R., Kong, Lingju, Wang, Min
Format: Artikel
Sprache:eng
Schlagworte:
Approximation
Boundary value problems
Chebyshev approximation
Chebyshev polynomials
Collocation method
Derivatives
Integrals
Mathematical analysis
Polynomials
Riemann–Liouville fractional calculus
Spectral methods
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Beschreibung
Zusammenfassung:The authors derive a series of explicit formulas to approximate the Riemann–Liouville derivative and integral of arbitrary order by shifted Chebyshev polynomials. This is then applied to solve boundary value problems involving Riemann–Liouville derivatives.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2014.05.012