In this paper, a two-dimensional time-fractional telegraph equation is considered with
derivative in the sense of Caputo and $1<\beta< 2$. The aim of this work is to extend the …

This study presents a novel high-order numerical method designed for solving the two-
dimensional time-fractional convection-diffusion (TFCD) equation. The Caputo definition is …

In this paper, a weakly coupled time-fractional one-dimensional system of Black-Scholes
equations is considered. To obtain a reliable approximation of the system solution, we …

This thesis focuses on the modification of the classical Black-Scholes equation by
introducing fractional derivatives instead of the usual integer order derivatives. The project …

A European option is one of the common types of options in financial markets, which can be
modeled by a time‐fractional parabolic PDE, known as the time‐fractional Black–Scholes …

Based on the time-fractional Black-Scholes pricing model, the evaluation of an American-
style option problem can be formulated as a free boundary problem. It is equivalent to a time …

The time-fractional Black-Scholes (TFBS) model is often used in the modeling of the
fractional structure observed in financial markets. In this paper we propose a high-order …

In this paper, radial basis functions (RBFs) method was used to solve a fractional Black‐
Scholes‐Schrodinger equation in an option pricing of financial problems. The RBFs method …

Chapter 2 presents numerical algorithms for the Riesz-space fractional partial differential
equations based on the combination of finite difference and operational matrix technique. In …

abstract In this paper, we aim at developing improved L1 operator splitting method and
spectral method for Black–Scholes differential systems with fractional derivatives in both …