This article applies efficient methods, namely, modified decomposition method and new
iterative transformation method, to analyze a nonlinear system of Korteweg–de Vries …

In this article, we investigate the nonlinear model describing the various physical and
chemical phenomena named the Kuramoto–Sivashinsky equation. We implemented the …

In this study, numerical results of a fractional-order multi-dimensional model of the Navier–
Stokes equations will be achieved via adoption of two analytical methods, ie, the Adomian …

In this paper, we used the natural decomposition approach with non-singular kernel
derivatives to find the solution to nonlinear fractional Gardner and Cahn–Hilliard equations …

In this article, we have investigated the fractional-order Burgers equation via Natural
decomposition method with nonsingular kernel derivatives. The two types of fractional …

This article presents a homotopy perturbation transform method and a variational iterative
transform method for analyzing the fractional-order non-linear system of the unsteady flow of …

In this article, the new iterative transform technique and homotopy perturbation transform
method are applied to calculate the fractional‐order Cauchy‐reaction diffusion equation …

In this paper, we introduce and implement the optimal auxiliary function method to solve a
system of fractional-order Whitham–Broer–Kaup equations, a class of nonlinear partial …

In the present research article, we implemented two well-known analytical techniques to
solve fractional-order multi-dimensional Navier–Stokes equation. The proposed methods …

In this article, the ρ-Laplace transform is paired with a new iterative method to create a new
hybrid methodology known as the new iterative transform method (NITM). This method is …