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

C. Vijayan, R. Manimaran and N. Racshitha

International Journal of Mathematics in Operational Research, 2025, vol. 30, issue 2, 135-151

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. (search for similar items in EconPapers)
Date: 2025
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