University of Tabriz Computational Methods for Differential Equations 2345-3982 12 4 2024 09 01 Lie symmetry analysis, and exact solutions to the time–fractional Black–Scholes equation of the Caputo–type 638 650 18174 10.22034/cmde.2024.59096.2510 EN 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. Journal Article 2023 11 06 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 https://cmde.tabrizu.ac.ir/article_18174_a1c0ab95666569fe9a4ad2c8a006b26b.pdf