In this paper we consider the following fractional differentiation problem: given noisy data to , approximate the fractional derivative for , which is the solution of the integral equation of first kind . Assuming and (where denotes the usual Sobolev norm of order ) we answer the question concerning the best possible accuracy for identifying from the noisy data . Furthermore, we discuss special regularization methods which realize this best possible accuracy.
Cite this article
Ulrich Tautenhahn, Rudolf Gorenflo, On Optimal Regularization Methods for Fractional Differentiation. Z. Anal. Anwend. 18 (1999), no. 2, pp. 449–467