This research apparatuses an approximate spectral method for the nonlinear time-fractional
partial integro-differential equation with a weakly singular kernel (TFPIDE). The main idea of …

In this study, we present an innovative approach involving a spectral collocation algorithm to
effectively obtain numerical solutions of the nonlinear time-fractional generalized Kawahara …

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, 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 …

Herein, we propose new efficient spectral algorithms for handling the fractional diffusion
wave equation (FDWE) and fractional diffusion wave equation with damping (FDWED). In …

A new numerical scheme based on the tau spectral method for solving the linear hyperbolic
telegraph type equation is presented and implemented. The derivation of this scheme is …

In this article, we present two numerical methods for treating the fractional initial‐value
problem (FIVP) and time‐fractional partial differential problem (FPDP) that caused the error …

Herein, a spectral Galerkin method for solving the fractional Rayleigh–Stokes problem
involving a nonlinear source term is analyzed. Two kinds of basis functions that are related …

The principal objective of this article is to develop new formulas of the so-called Chebyshev
polynomials of the fifth-kind. Some fundamental properties and relations concerned with …