Caputo fractional derivative estimation for a class of signals satisfying a linear differential equation

This paper aims at estimating the Caputo fractional derivatives for a class of signals satisfying a linear differential equation. For this purpose, an estimator for the initial conditions of the studied signal and an fractional order differentiator for the Riemann-Liouville fractional derivatives are needed. Firstly, an algebraic integral formula for the initial conditions is introduced using a generalized modulating functions method. Then, an estimator for the initial conditions is derived using a numerical integration method in discrete noisy case. Finally, a numerical example illustrates the accuracy and the robustness of the proposed method, where a recent fractional order differentiator for the Riemann-Liouville fractional derivatives is considered.