Invariant subspace method for fractional Black-Scholes equations

In this paper, the invariant subspace method is used to solve the time- and pricing-fractional Black-Scholes equations, in which the fractional derivatives are described in the Caputo and Weyl sense, respectively. We introduce invariant subspaces for time and pricing differential operators. Applying an appropriate invariant subspace will reduce the fractional Black-Scholes equation to a system of ordinary fractional differential equations. Finally, using point symmetries of the obtained system, we construct the explicit solutions of the fractional Black-Scholes equations.