In 2009, Bell and Stelljes described a method for constructing a class of solvable arbitrage-free models for stock prices. As a result, a second-order partial differential equation that is similar to the classical Black-Scholes equation was yielded and two solutions of the equation were given. Later in 2016, Sinkala extended this result using the Lie symmetry analysis. In this paper, Sinkala's work is extended to a time fractional arbitrage-free stock price model using the Lie symmetry analysis. Employing the algorithmic package developed by Jefferson, the determining equations of the fractional model are solved. Finally an optimal system and some examples of invariant solutions are presented.