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 …

In this research, we present a new computational technique for solving some physics
problems involving fractional-order differential equations including the famous Bagley …

The time-fractional diffusion equation is applied to a wide range of practical applications. We
suggest using a potent spectral approach to solve this equation. These techniques' main …

This research is concerned to some modernistic wave solutions of truncated M-fractional
new Hamiltonian amplitude (NHA) equation. The dealing model relates with some …

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, we build and implement a combination of Lucas polynomials basis that fulfills the
spatial homogenous boundary conditions. This basis is then used to solve the time-fractional …

A Numerical solution of the Caputo-time and Riesz-space fractional reaction–diffusion
model is considered in this paper. Based on finite difference schemes, we formulate both …

In this study, a spectral tau solution to the heat conduction equation is introduced. As basis
functions, the orthogonal polynomials, namely, the shifted fifth-kind Chebyshev polynomials …

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 …