In this paper, we develop a numerical scheme based on two-dimensional orthonormal
Bernstein polynomials (2D-OBPs) to solve two-dimensional nonlinear integral equations of …

This work develops a new Legendre delay operational matrix based on Legendre
polynomial features that are integrated with regard to the Legendre fractional derivative …

In this paper, the nonlinear space–time fractal–fractional advection–diffusion–reaction
equation is introduced and a highly accurate methodology is presented for its numerical …

This article defines a novel version of nonlinear fourth‐order diffusion‐wave equation, which
involves variable‐fractional differentiations with nonsingular kernel. This newly defined …

This paper provides a technique to investigate the inverse Laplace transform by using
orthonormal Bernstein operational matrix of integration. The proposed method is based on …

Currently, a study has come out with a novel class of differential operators using fractional-
order and variable-order fractal Atangana–Baleanu derivative, which in turn, became the …

This paper introduces two novel methods for solving multi-order fractional differential
equations using Bernstein polynomials. The first method, referred to as the fractional …

This paper presents two methods for solving two‐dimensional linear and nonlinear time‐
fractional advection–diffusion equations with Caputo fractional derivatives. To effectively …

In this paper, we propose an approximate solution method, called multistage Bernstein
collocation method (MBCM), to solve strongly nonlinear damped systems. The method is …

A numerical technique for one-dimensional Bratu's problem is displayed in this work. The
technique depends on Bernstein polynomial approximation. Numerical examples are …