Applied Mathematics and Computation 270 (2015) 44–46 Contents lists available at ScienceDirect Applied Mathematics and Computation journal homepage: www.elsevier.com/locate/amc Comments on “Discretization of fractional order differentiator over Paley–Wiener space” Manuel D. Ortigueira * UNINOVA and DEE of Faculdade de Ciências e Tecnologia da UNL, Campus da FCT da UNL, Quinta da Torre, 2829-516 Caparica, Portugal article info Keywords: Fractional derivative Bandlimited functions Paley–Wiener space Grünwald–Letnikov derivative abstract It is shown that the definitions underlying the algorithm proposed in Wu (2014) are not suit- able for supporting the algorithm. Suitable definitions are presented. © 2015 Elsevier Inc. All rights reserved. 1. Introduction In [1], Wu presented an interesting algorithm for designing finite impulse filters suitable for approximating fractional deriva- tives of bandlimited functions. The algorithm is very simple and only has one assumption: the frequency response of an order α fractional derivative operator is (iω) α . With this the author was able to obtain the coefficients of the filter. From algorithmic point of view the paper does not raise any questions. However the definitions and examples deserve some comments. 1. On the defined fractional derivatives Assume that f(t) is a real variable “enough good” function to ensure the existence of the derivatives. Attending to our objec- tives we can assume that it is absolutely integrable, guaranteeing it has Fourier transform. In Section 2 [1], three fractional derivatives, say, Riemann–Liouville, Caputo, and Grünwald–Letnikov are defined [5] • Riemann–Liouville D α f (t ) = 1 Ŵ(n - α) d n dt n  t α f (τ )(t - τ) n-α-1 dτ (1) where n - 1 ≤ α < n. • Caputo D α f (t ) = 1 Ŵ(n - α)  t α f (n) (τ )(t - τ) n-α-1 dτ (2) • Grünwald–Letnikov D α f (t ) = lim h→0+ N ∑ n=0 (-1) n ( α n ) f (t - nh) h α (3) where h > 0 and N = [ t -α h ]; [.] means “the integer part” [3]. * Tel.: +351212948520. E-mail address: mdo@fct.unl.pt http://dx.doi.org/10.1016/j.amc.2015.08.044 0096-3003/© 2015 Elsevier Inc. All rights reserved.