In this paper we consider multi variable orders differential equations (MVODEs) with non-
local and no-singular kernel. The derivative is described in Atangana and Baleanu sense of …

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

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 …

The basic aim of this paper is to develop new numerical algorithms for solving some linear
and nonlinear fractional-order differential equations. We have developed a new type of …

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

This paper presents an explicit formula that approximates the fractional derivatives of
Chebyshev polynomials of the first-kind in the Caputo sense. The new expression is given in …

This paper is dedicated to implementing and presenting numerical algorithms for solving
some linear and nonlinear even-order two-point boundary value problems. For this purpose …

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 …