SOLUTION OF TIME-FRACTIONAL BLACK–SCHOLES EQUATIONS VIA HOMOTOPY ANALYSIS SUMUDU TRANSFORM METHOD

Hongliang Gao, Rishi Kumar Pandey, Ram Kishun Lodhi and Hossein Jafari
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Hongliang Gao: School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou, P. R. China
Rishi Kumar Pandey: ��Symbiosis Centre for Management Studies (SCMS), Symbiosis International (Deemed University) (SIU), Mouza-Wathoda, Nagpur, Maharashtra, India
Ram Kishun Lodhi: ��Symbiosis Institute of Technology, Pune Campus, Symbiosis International (Deemed University) (SIU), Pune 412115, Maharashtra, India
Hossein Jafari: �Department of Applied Mathematics, University of Mazandaran, Babolsar, Iran¶Department of Mathematical Sciences, University of South Africa, UNISA0003, South Africa∥Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 110112, Taiwan

FRACTALS (fractals), 2025, vol. 33, issue 06, 1-11

Abstract: This study presents a semi-analytical solution to the time-fractional Black–Scholes equation (TFBSE) using the homotopy analysis fractional Sumudu transform method (HAFSTM). The solutions obtained for the TFBSE are matched through exact solutions to demonstrate the impact of fractional order. The results confirm that this approach is highly reliable and effective, offering a flexible and accurate way to solve the equation without constraints such as finite discretization, limited domain, or perturbation methods.

Keywords: Fractional Derivative; Homotopy Analysis Fractional Sumudu Transform Method; Black–Scholes Option Pricing Equation (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X25401103

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