This work deals with the put option pricing problems based on the time-fractional Black-Scholes equation, where the fractional derivative is a so-called modified Riemann-Liouville fractional derivative. With the aid of symbolic calculation software, European and American put option pricing models that combine the time-fractional Black-Scholes equation with the conditions satisfied by the standard put options are numerically solved using the implicit scheme of the finite difference method.
"Solution of the Fractional Black-Scholes Option Pricing Model by Finite Difference Method." Abstr. Appl. Anal. 2013 1 - 10, 2013. https://doi.org/10.1155/2013/194286