University of Guilan Journal of Mathematical Modeling 2345-394X 12 3 2024 09 01 An efficient numerical method based on cubic B--splines for the time--fractional Black--Scholes European option pricing model 405 417 7677 10.22124/jmm.2024.26551.2341 EN Hamed Payandehdoost Masouleh Department of Accounting, Bandaranzali Branch, Islamic Azad University, Bandaranzali, Iran 0000-0002-9578-0702 Mojgan Esmailzadeh Department of Applied Mathematics, Bandaranzali Branch, Islamic Azad University, Bandaranzali, Iran Journal Article 2024 01 22 In this study, we develop a precise and effective numerical approach to solve the time--fractional Black--Scholes equation, which is used to calculate European options. The method employs cubic B-spline collocation for spatial discretization and a finite difference method for time discretization. An  analysis of the method's stability is conducted. Finally, two numerical examples are included to show the effectiveness and applicability of the suggested method. https://jmm.guilan.ac.ir/article_7677_54cb32864ccf7e134e2b8acef3dd8c9e.pdf