Title: Fractional Black-Scholes equation described by the conformable fractional derivative with three different methods

Authors: C. Vijayan; R. Manimaran; N. Racshitha

Addresses: Department of Mathematics, Faculty of Engineering and Technology, SRM Institute of Science and Technology, Vadapalani Campus, No. 1 Jawaharlal Nehru Salai, Vadapalani, Chennai – 600026, Tamil Nadu, India ' Department of Mathematics, Faculty of Engineering and Technology, SRM Institute of Science and Technology, Vadapalani Campus, No. 1 Jawaharlal Nehru Salai, Vadapalani, Chennai – 600026, Tamil Nadu, India ' Department of Mathematics, Faculty of Engineering and Technology, SRM Institute of Science and Technology, Vadapalani Campus, No. 1 Jawaharlal Nehru Salai, Vadapalani, Chennai – 600026, Tamil Nadu, India

Abstract: This study deals with the conformable fractional derivative (CFD) operator and three different methods for solving the fractional Black-Scholes equation (FBSE) and the generalised fractional Black-Scholes equation (GFBSE). They are the variation iteration method (VIM), reduced differential transform method (RDTM) and homotopy analysis method (HAM). The redefined proposed methods are the conformable variation iteration method (CVIM), conformable fractional reduced differential transform method (CRDTM), and conformable homotopy analysis method (CHAM). Finally, images and tables are used to display the results of FBSE and GFBSE. These methods can be used to accurately solve both the fractional Black-Scholes equation and the generalised fractional Black-Scholes equation.

Keywords: Black-Scholes equation; BSE; conformable fractional derivative; CFD; variational iteration method; VIM; reduced differential transform method; RDTM; homotopy analysis methods; HAM.

DOI: 10.1504/IJMOR.2025.145604

International Journal of Mathematics in Operational Research, 2025 Vol.30 No.2, pp.135 - 151

Received: 19 Jul 2023
Accepted: 21 Jul 2023
Published online: 09 Apr 2025 *

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