This paper is concerned with establishing novel expressions that express the derivative of
any order of the orthogonal polynomials, namely, Chebyshev polynomials of the sixth kind in …

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 …

The reduced version of the fractional Laplace transform, called the v-Laplac transform, is
used in combination with the Adomian decomposition method to generate approximate …

In this paper, the finite integration method and the operational matrix of fractional integration
are implemented based on the shifted Chebyshev polynomial. They are utilized to devise …

This paper provides a fruitful and effective spectral scheme based on the two-dimensional
Pell collocation method for treating of nonlinear time-fractional Burgers equations with …

This paper presents an explicit formula of conditional expectation for a product of polynomial
functions and the discounted characteristic function based on the Cox–Ingersoll–Ross (CIR) …

The main goal of this article is to investigate theoretically a kind of orthogonal polynomials,
namely, generalized Jacobi polynomials (GJP s). These polynomials can be expressed as …

A numerical approach to approximate the nonlinear Burgers' equation solution is presented
in this article. By temporally discretizing the problem using the Crank-Nicolson scheme, we …

This paper proposes a simple and novel approach based on solving a partial differential
equation (PDE) to establish the concise analytical formulas for a conditional moment and …

In this paper, we combine the finite integration method (FIM) with the technique of fictitious
points to solve high order partial differential equations (HOPDEs). Two type of fictitious finite …