Recently, Mboup, Join and Fliess [27], [28] introduced non-asymptotic integer
order differentiators by using an algebraic parametric estimation method [7],
[8]. In this paper, in order to obtain non-asymptotic fractional order
differentiators we apply this algebraic parametric method to truncated
expansions of fractional Taylor series based on the Jumarie's modified
Riemann-Liouville derivative [14]. Exact and simple formulae for these
differentiators are given where a sliding integration window of a noisy signal
involving Jacobi polynomials is used without complex mathematical deduction.
The efficiency and the stability with respect to corrupting noises of the
proposed fractional order differentiators are shown in numerical simulations
