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Discretized fractional calculus. (English) Zbl 0624.65015
Es werden für Fraktionalintegrale der Form 0 x (x-s) α-1 x β-1 g(x)ds Konvolutionsquadraturen untersucht, d.h. numerische Näherungen in den Punkten x=0,h,2h,···Nh bestimmt. Es wird gezeigt, daß die angegebenen Methoden konvergent von der Ordnung p sind, wenn sie stabil und von der Ordnung p konsistent sind. Schließlich werden einige numerische Beispiele und Anwendungen angegeben, wie die Behandlung der Abelschen Integralgleichung, das Diffusionsproblem (Wärmeleitung im Halbraum) und die Berechnung von speziellen Funktionen der mathematischen Physik.
Reviewer: H.F.Bauer

MSC:
65D32Quadrature and cubature formulas (numerical methods)
41A55Approximate quadratures
65D20Computation of special functions, construction of tables
65R20Integral equations (numerical methods)
65D25Numerical differentiation
30E20Integration, integrals of Cauchy type, etc. (one complex variable)
26A33Fractional derivatives and integrals (real functions)
33B15Gamma, beta and polygamma functions