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Galerkin-finite difference method for fractional parabolic partial differential equations [PDF]
MethodsXThe fractional form of the classical diffusion equation embodies the super-diffusive and sub-diffusive characteristics of any flow, depending on the fractional order. This study aims to approximate the solution of parabolic partial differential equations
Md. Shorif Hossan +2 more
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Mathematics, 2021 In the finance market, it is well known that the price change of the underlying fractal transmission system can be modeled with the Black-Scholes equation.
Sivaporn Ampun, Panumart Sawangtong
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Analytical solution of time-fractional N-dimensional Black-Scholes equation using LHPM
Ratio Mathematica, 2023 A famous Black-Scholes differential equation is used for pricing options in financial world which represents financial derivatives more significantly. Option is one of the crucial financial derivatives. Sawangtong P., Trachoo K., Sawangtong W.
Sanjay Ghevariya, CHETANBHAI PATEL
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Computation, 2021 In the finance market, the Black–Scholes equation is used to model the price change of the underlying fractal transmission system. Moreover, the fractional differential equations recently are accepted by researchers that fractional differential equations
Sirunya Thanompolkrang +2 more
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Alexandria Engineering Journal, 2023 Trivially, the time-fractional Black–Scholes (FBS) equation is utilized to describe the behavior of the option pricing in financial markets. This work is intended as an attempt to introduce the ψ-Hilfer fractional Black–Scholes (ψ-HFBS) equation.
F. Mohammadizadeh +4 more
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Nonuniform Finite Difference Scheme for the Three-Dimensional Time-Fractional Black–Scholes Equation
Journal of Function Spaces, 2021 In this study, we present an accurate and efficient nonuniform finite difference method for the three-dimensional (3D) time-fractional Black–Scholes (BS) equation.
Sangkwon Kim +5 more
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Fractal and Fractional, 2023 In this paper, we consider an approximation of the Caputo fractional derivative and its asymptotic expansion formula, whose generating function is the polylogarithm function.
Yuri Dimitrov +2 more
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On the solution of two-dimensional fractional Black–Scholes equation for European put option
Advances in Difference Equations, 2020 The purpose of this paper was to investigate the dynamics of the option pricing in the market through the two-dimensional time fractional-order Black–Scholes equation for a European put option.
Din Prathumwan, Kamonchat Trachoo
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On a Multigrid Method for Tempered Fractional Diffusion Equations
Fractal and Fractional, 2021 In this paper, we develop a suitable multigrid iterative solution method for the numerical solution of second- and third-order discrete schemes for the tempered fractional diffusion equation.
Linlin Bu, Cornelis W. Oosterlee
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A robust numerical solution to a time-fractional Black–Scholes equation
Advances in Difference Equations, 2021 Dividend paying European stock options are modeled using a time-fractional Black–Scholes (tfBS) partial differential equation (PDE). The underlying fractional stochastic dynamics explored in this work are appropriate for capturing market fluctuations in ...
S. M. Nuugulu, F. Gideon, K. C. Patidar
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