The principal aim of the current paper is to present and analyze two new spectral algorithms
for solving some types of linear and nonlinear fractional-order differential equations. The …

The aim of this paper is to apply the newly trending Atangana-Baluanu derivative operator to
model some symbiosis systems describing commmensalism and predator-prey processes …

Through the current article, a numerical technique to obtain an approximate solution of one-
dimensional linear hyperbolic partial differential equations is implemented. A certain …

The time-fractional heat equation governed by nonlocal conditions is solved using a novel
method developed in this study, which is based on the spectral tau method. There are two …

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 paper, we study and present a spectral numerical technique for solving a general
class of multi-order fractional pantograph equations with varying coefficients and systems of …

This study is to introduce a novel design and implementation of a neuro-swarming
computational numerical procedure for numerical treatment of the fractional Bagley–Torvik …

This paper concerns new numerical solutions for certain coupled system of fractional
differential equations through the employment of the so-called generalized Fibonacci …

The primary point of this manuscript is to dissect and execute a new modified Galerkin
algorithm based on the shifted Jacobi polynomials for solving fractional differential …

The current manuscript introduces a novel numerical treatment for multi-term fractional
differential equations with variable coefficients. The spectral Galerkin approach is developed …