Document Type

Journal Article

Department/Unit

Department of Mathematics

Abstract

Previously, based on the method of (radial powers) radial basis functions, we proposed a procedure for approximating derivative values from one-dimensional scattered noisy data. In this work, we show that the same approach also allows us to approximate the values of (Caputo) fractional derivatives (for orders between 0 and 1). With either an a priori or a posteriori strategy of choosing the regularization parameter, our convergence analysis shows that the approximated fractional derivative values converge at the same rate as in the case of integer order 1.

Publication Year

2015

Journal Title

Journal of Scientific Computing

Volume number

62

Issue number

1

Publisher

Springer Verlag

First Page (page number)

300

Last Page (page number)

315

Referreed

1

DOI

10.1007/s10915-014-9857-6

ISSN (print)

08857474

Keywords

Fractional derivatives, inverse problem, convergence analysis, noisy data, regularization

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