The price variation of the correlated fractal transmission system is used to deduce the
fractional Black–Scholes model that has an α α-order time fractional derivative. The …

This paper presents an explicit formula that approximates the fractional derivatives of
Chebyshev polynomials of the first-kind in the Caputo sense. The new expression is given in …

This paper is devoted to developing spectral solutions for the nonlinear fractional Klein–
Gordon equation. The typical collocation method and the tau method are employed for …

In this paper, we propose and analyze a novel spectral scheme for the numerical solution of
a two-dimensional time-fractional diffusion equation. The proposed scheme approximates …

In this paper, our target is to implement and analyze numerical algorithms for the numerical
solutions of initial and boundary third-order singular-type equations, and in particular the …

The main goal of this paper is to develop a new formula of the fractional derivatives of the
shifted Chebyshev polynomials of the third kind. This new formula expresses approximately …

This paper proposes the alternating direction implicit (ADI) numerical approaches for
computing the solution of multi-dimensional distributed-order fractional integrodifferential …

In this article, a numerical technique based on polynomials is proposed for the solution of
one and two-dimensional time-fractional Burgers equation. First, the given problem is …

This paper presents a numerical solution of the temporal-fractional Black–Scholes equation
governing European options (TFBSE-EO) in the finite domain so that the temporal derivative …

Herein, we construct an explicit modal numerical solver based on the spec-tral Petrov–
Galerkin method via a specific combination of shifted Cheby-shev polynomial basis for …