846107.fig.002a
(a)
846107.fig.002b
(b)
846107.fig.002c
(c)
Figure 2: Plots of the 𝑡 derivatives of erfc ( 𝑡 ) . The points are the 0- and 1st-order derivatives at 𝑡 = 0 and 𝑡 = 1 . Also shown for comparison is the 𝑡 derivative from Coimbra's operator (2.15) (dashed line). (a) Riemann-Liouville type operator (2.13) with 𝑞 ( 𝑡 , 𝜎 ) = 𝑞 ( 𝑡 ) (thin line), 𝑞 ( 𝜎 ) (medium line), 𝑞 ( 𝑡 𝜎 ) (thick line). (b) Caputo-type definition (2.14) with 𝑞 ( 𝑡 , 𝜎 ) = 𝑞 ( 𝑡 ) (thin line), 𝑞 ( 𝜎 ) (medium line), 𝑞 ( 𝑡 𝜎 ) (thick line). In this case the operator (2.14) with exponent 𝑞 ( 𝑡 ) does not match Coimbra's operator, but is equivalent to the first derivative at 𝑡 = 1 . (c) Definition (2.11) (thin line).