The propose of this research is to apply a novel numerical learning approximation of time-
fractional sub diffusion model on a semi-infinite domain. This model is a nonlinear fractional …

Generalized Jacobi polynomials with indexes α, β ∈ R α, β∈ R are introduced and some
basic properties are established. As examples of applications, the second-and fourth-order …

Fully diagonalized spectral methods using Sobolev orthogonal/biorthogonal basis functions
are proposed for solving second order elliptic boundary value problems. We first construct …

In this paper, we introduce three series of Jacobi rational basis functions on the half line by
using the matrix decomposition technique. The new basis functions are simultaneously …

The main aim of this paper is to investigate Sobolev orthogonality and families of orthogonal
polynomials on the triangle as a generalization of the results in Xu, Y. Constr. Approx. 46 …

Diagonalized Chebyshev rational spectral methods for solving second-order elliptic
problems on the half/whole line are proposed. Some Sobolev bi-orthogonal rational basis …

In this paper we will discuss asymptotic properties of monic polynomials {S n λ (x)} n≥ 0
orthogonal with respect to the Sobolev inner product< p, q> S=∫ R p (x) q (x) d μ 0+ λ∫ R …

Laguerre polynomials are orthogonal polynomials defined on positive half line with respect
to weight $ e^{-x} $. They have wide applications in scientific and engineering computations …

Hermite spectral methods using Sobolev orthogonal/biorthogonal basis functions for solving
second and fourth-order differential equations on unbounded domains are proposed. Some …

Modified Legendre rational spectral methods for solving second‐order differential equations
on the half line are proposed. Some Sobolev orthogonal Legendre rational basis functions …