High-accuracy numerical integration methods for fractional order derivatives and integrals computations

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dc.contributor.authorBrzeziński, Dariusz W.
dc.contributor.authorOstalczyk, Piotr
dc.date.accessioned2016-02-03T11:20:14Z
dc.date.available2016-02-03T11:20:14Z
dc.date.issued2014
dc.description.abstractIn this paper the authors present highly accurate and remarkably efficient computational methods for fractional order derivatives and integrals applying Riemann-Liouville and Caputo formulae: the Gauss-Jacobi Quadrature with adopted weight function, the Double Exponential Formula, applying two arbitrary precision and exact rounding mathematical libraries (GNU GMP and GNU MPFR). Example fractional order derivatives and integrals of some elementary functions are calculated. Resulting accuracy is compared with accuracy achieved by applying widely known methods of numerical integration. Finally, presented methods are applied to solve Abel’s Integral equation (in Appendix).en_EN
dc.identifier.citationBulletin of the Polish Academy of Sciences Technical Sciences, Vol. 62, Issue 4, 2014, Pages 723–733
dc.identifier.urihttp://hdl.handle.net/11652/1072
dc.identifier.urihttp://www.degruyter.com/view/j/bpasts.2014.62.issue-4/bpasts-2014-0078/bpasts-2014-0078.xml?format=INT
dc.language.isoenen_EN
dc.relation.ispartofseriesBulletin of the Polish Academy of Sciences Technical Sciences, Vol. 62, Issue 4, 2014en_EN
dc.subjectaccuracy of numerical calculationsen_EN
dc.subjectfractional order derivatives and integralsen_EN
dc.subjectdouble exponential formulaen_EN
dc.subjectgauss-jacobi quadrature with adopted weight functionen_EN
dc.subjectarbitrary precisionen_EN
dc.subjectnumerical integrationen_EN
dc.subjectabel’s integral equationen_EN
dc.titleHigh-accuracy numerical integration methods for fractional order derivatives and integrals computationsen_EN
dc.typeArtykułpl_PL
dc.typeArticleen_EN

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