The pioneering work in finance by Black, Scholes and Merton during the 1970s led to the
emergence of the Black-Scholes (BS) equation, which offers a concise and transparent …

In this paper, we propose a collocation scheme for efficiently solving the mixed time-
fractional Black-Scholes (MTF-BS) model and obtaining the option price. Our approach …

In this paper, two high-order compact difference schemes with graded meshes are proposed
for solving the time-fractional Black-Scholes equation. We first eliminate the convection term …

This paper presents an efficient numerical approach employing RBF-HFD to tackle fractional
option pricing. This scheme as an extension of the RBF-FD technique, offers solutions for …

In this paper, we are concerned with the convergence rates of an implicit-explicit (IMEX)
difference scheme for solving a two-dimensional partial integro-differential equation (PIDE) …

Because of the high approximation power and simplicity of computation of smooth radial
basis functions (RBFs), in recent decades they have received much attention for function …

In this work, we propose a fast scheme based on higher order discretizations on graded
meshes for resolving the temporal-fractional partial differential equation (PDE), which …

When solving time fractional partial integro-differential equations (PIDEs) using standard
finite difference methods, we have to invert the dense matrices arising from the discretization …

In this paper, we considered the two-dimensional fractional-order Black-Scholes model in
the Liouville-Caputo sense. The Black-Scholes model was an important tool in the financial …

In this paper, Multiquadric quasi-interpolation method is used to approximate fractional
integral equations and fractional differential equations. Firstly, we construct two operators for …