Ramin Najafi - Department of Mathematics, Maku Branch, Islamic Azad University, Maku, Iran.
Fariba Bahrami - Faculty of Mathematics and Computer Science, University of Tabriz, Tabriz, Iran.
Parisa Vafadar - Faculty of Mathematics and Computer Science, University of Tabriz, Tabriz, Iran.

In this study, the Lie symmetry analysis, and exact solutions are investigated to the fractional Black–Scholes(B-S) equations of the Caputo–type modeling of the pricing options under the absence of arbitrage and self-financing portfolio assumptions. A class of exact invariant and solitary solutions are given to B-S equations. Some examples are presented in which we use the obtained reductions to find their exact solutions.

Lie symmetry analysis, Time–fractional Black–Scholes equation, Caputo fractional derivative, Invariant solutions