Suppose you need to find the fractional European call and the fractional European put options. Let the Hurst parameter be $H=0.85$, the $\sigma=0,25$, $r=0.10$, $S_{fbm} = 100$, $K = 95$, we have \begin{eqnarray*} d_1^{fBm} & = & \frac{\ln{\frac{S}{K}} + \frac{1}{2}(r( T - t) + \frac{(1)\sigma^2{( T^{2H} - t^{2H})}}{2})}{\sigma{\sqrt{T^{2H} - t^{2H}}}}\\ & = & \frac{\ln(\frac{105}{100}) + (0.10(0.25 -0) + \frac{(1){0.25^2}{0.25^{2(0.85)} - (1)0.25^{2(0.85)}}}{2}}{(0.25){\sqrt{0.25^{2(0.85)} - 0}})} \end{eqnarray*} we obtain $d^{fBm}_1= 1.0558$. We find in the normal distribution that $N(1.0558)= 0.8544$ and $N(-1.0558) = 0.1456.$ \begin{eqnarray*} d_2^{fBm} & = & \frac{\ln{\frac{S}{K}} + \frac{1}{2}(r( T - t) - \frac{\sigma^2{( T^{2H}