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Rafei, M. and Ganji, D. (2006) Explicit Solutions of Helmholtz Equation and Fifth-Order KdV Equation Using Homotopy Perturbation Method. International Journal of Nonlinear Sciences and Numerical Simulation, 7, 321-328.
https://doi.org/10.1515/IJNSNS.2006.7.3.321

has been cited by the following article:

• TITLE: Exact Solution of Fractional Black-Scholes European Option Pricing Equations

  AUTHORS: Maryeme Ouafoudi, Fei Gao

  KEYWORDS: Homotopy Perturbation Method, Modified Homotopy Perturbation Method, Sumudu Transform, Black-Scholes Equations

  JOURNAL NAME: Applied Mathematics, Vol.9 No.1, January 30, 2018

  ABSTRACT: We introduce two algorithms in order to find the exact solution of the nonlinear Time-fractional Partial differential equation, in this research work. Those algorithms are proposed in the following structure: The Modified Homotopy Perturbation Method (MHPM), The Homotopy Perturbation and Sumudu Transform Method. The results achieved using the both methods are the same. However, we calculate the approached theoretical solution of the Black-Scholes model in the form of a convergent power series with a regularly calculated element. Finally, we propose a descriptive example to demonstrate the efficiency and the simplicity of the methods.