The computation of Caputo fractional derivatives is an ill-posed problem (in fact a special deconvolution problem) which can be approached using suitable regularization methods. Recent applications of deconvolution problems in control theory require recursive regularization methods. For this reason we present here a recursive method for the computation of an approximant v(t) of the Caputo fractional derivative (D^α_*f)(t), which is an extension of the usual Lavrent'ev method ( is the regularization parameter). In applications to control theory the signal f whose derivative has to be computed is measured at discrete time instants kτ. In this case the algorithm we propose updates the value of v at the times kτ when the new measure of the signal f(t) is received. The algorithm can be applied to fractional (and integer) derivatives of any order.

02.60.-x Numerical approximation and analysis

65F22 Ill-posedness, regularization

Computational physics

Issue 1 (February 2008)

Received 2 July 2007 , in final form 19 December 2007

Published 16 January 2008