Before revision:  The time-fractional partial differential equation appears in several diffusion problems used in physics and engineering applications . Using some of these ideas we numerical compute solutions of the fractional Black-Scholes formula that is used as a model for valuing call and put options on a paying stock. Time-fractional Black-Scholes models subdiffusive and superdiffusive behavior of the prices at the stock market  .
After revision:  The time-fractional partial differential equation appears in several diffusion problems used in physics and engineering applications , and models subdiffusive and superdiffusive behavior of the prices at the stock market .