Diethelm, K. Peano kernels of non-integer order. (English) Zbl 0880.41022 Z. Anal. Anwend. 16, No. 3, 727-738 (1997). Summary: We consider the representation of error functionals in numerical quadrature by the Peano kernel method. It is easily observed that the usual expressions for Peano kernels of order \(s\) still make sense if \(s\) is not a natural number. In this paper, we discuss how to interpret these Peano kernels, we state their main properties, and we compare them to the (classical) Peano kernels of integer order. Cited in 2 Documents MSC: 41A55 Approximate quadratures 26A33 Fractional derivatives and integrals Keywords:error bounds; fractional calculus; Peano kernels PDFBibTeX XMLCite \textit{K. Diethelm}, Z. Anal. Anwend. 16, No. 3, 727--738 (1997; Zbl 0880.41022) Full Text: DOI References: [1] Linz, P.: Analytical and Numerical Methods for Volterra Equations. Philadelphia, PA: SIAM 1985. · Zbl 0566.65094 [2] Peano, C.: Resto nelle forinule di quadrature, espresso con un integrate definito. Atti Accad. Lincei Cl. Sci. Fis. Mat. Natur. Rend. (5) 22 (1913), 562 - 569. · JFM 44.0358.02 [3] Powell, M. J. D.: Approximation Theory and Methods. Cambridge: Univ. Press 1981. · Zbl 0453.41001 [4] Samko, S. G., Kilbas, A. A. and 0. 1. Marichev: Fractional Integrals and Derivatives: Theory and Applications. Yverdon: Gordon and Breach 1993. · Zbl 0818.26003 [5] Sard, A.: Linear Approximation (Math. Surveys and Monographs: Vol. 9). 2nd printing with corrections. Providence, R.I.: Amer. Math. Soc. 1982. · Zbl 0115.05403 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.