Figure 1: Plots of the derivatives of . The points are the and 1st-order fractional derivatives at . (a) Definition (2.13) with (thin line), (medium line), and (thick line). Note that none of the definitions match the 1st-order derivative at . (b) Caputo-type VO operators (2.14) with (thin line), (medium line), and (thick line). Note that the variant of (2.14) with argument matches the corresponding fractional derivatives at . (c) Definition (2.11) (thick line) and Coimbra's operator (2.15) (thin line). The -derivative defined by (2.15) is equivalent to the corresponding fractional derivatives at all the points.