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

被引：0
|
作者：
Gao, Hongliang [1 ]
Pandey, Rishi kumar [2 ]
Lodhi, Ram kishun [3 ]
Jafari, Hossein [4 ,5 ,6 ]
机构：
[1] Lanzhou Jiaotong Univ, Sch Math & Phys, Lanzhou, Peoples R China
[2] Symbiosis Int Deemed Univ SIU, Symbiosis Ctr Management Studies SCMS, Nagpur, Maharashtra, India
[3] Symbiosis Int Deemed Univ SIU, Symbiosis Inst Technol, Pune Campus, Pune 412115, Maharashtra, India
[4] Univ Mazandaran, Dept Appl Math, Babolsar, Iran
[5] Univ South Africa, UNISA, Dept Math Sci, Pretoria 0003, South Africa
[6] China Med Univ, China Med Univ Hosp, Dept Med Res, Taichung, Taiwan
来源：
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY | 2025年
关键词：
Fractional Derivative; Homotopy Analysis Fractional Sumudu Transform Method; Black-Scholes Option Pricing Equation; PARTIAL-DIFFERENTIAL-EQUATIONS; BROWNIAN-MOTION; INTEGRAL TRANSFORM; ANALYTIC SOLUTION; CALCULUS; MODEL;
D O I：
10.1142/S0218348X25401103
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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.
引用
收藏
页数：11
相关论文
共 50 条
  • [31] Selection of shape parameter in radial basis functions for solution of time-fractional Black-Scholes models
    Haq, Sirajul
    Hussain, Manzoor
    APPLIED MATHEMATICS AND COMPUTATION, 2018, 335 : 248 - 263
  • [32] Touchard wavelet technique for solving time-fractional Black-Scholes model
    Nourian, Farshid
    Lakestani, Mehrdad
    Sabermahani, Sedigheh
    Ordokhani, Yadollah
    COMPUTATIONAL & APPLIED MATHEMATICS, 2022, 41 (04):
  • [33] A New Version of Black-Scholes Equation Presented by Time-Fractional Derivative
    Farhadi, A.
    Salehi, M.
    Erjaee, G. H.
    IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY TRANSACTION A-SCIENCE, 2018, 42 (A4): : 2159 - 2166
  • [34] Numerical solution of time-fractional Black–Scholes equation
    Miglena N. Koleva
    Lubin G. Vulkov
    Computational and Applied Mathematics, 2017, 36 : 1699 - 1715
  • [35] The homotopy perturbation method for the Black-Scholes equation
    Gulkac, Vildan
    JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION, 2010, 80 (12) : 1349 - 1354
  • [36] On the approximate solution of nonlinear time-fractional KdV equation via modified homotopy analysis Laplace transform method
    Li, Chong
    Kumarb, Amit
    Kumarb, Sunil
    Yang, Xiao-Jun
    JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS, 2016, 9 (09): : 5463 - 5470
  • [37] Solving Black–Scholes equations using fractional generalized homotopy analysis method
    S. R. Saratha
    G. Sai Sundara Krishnan
    M. Bagyalakshmi
    Chee Peng Lim
    Computational and Applied Mathematics, 2020, 39
  • [38] The Approximate Analytic Solution of the Time-Fractional Black-Scholes Equation with a European Option Based on the Katugampola Fractional Derivative
    Ampun, Sivaporn
    Sawangtong, Panumart
    MATHEMATICS, 2021, 9 (03) : 1 - 15
  • [39] A second order numerical method for the time-fractional Black-Scholes European option pricing model
    Kazmi, Kamran
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2023, 418
  • [40] Spectral Solutions for Fractional Black-Scholes Equations
    Abdelkawy, M. A.
    Lopes, Antonio M.
    MATHEMATICAL PROBLEMS IN ENGINEERING, 2022, 2022
12345