A Lavrent'ev-type approach to the on-line computation of Caputo fractional derivatives

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 vε(t) of the Caputo fractional derivative (Dα*f)(t), which is an extension of the usual Lavrent'ev method (ε 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 vε 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