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

Navier–Stokes (NS) equation, in fluid mechanics, is a partial differential equation that
describes the flow of incompressible fluids. We study the fractional derivative by using …

This article utilizes the Aboodh residual power series and Aboodh transform iteration
methods to address fractional nonlinear systems. Based on these techniques, a system is …

In this paper, fractional-order system gas dynamics equations are solved analytically using
an appealing novel method known as the Laplace residual power series technique, which is …

This paper aims to obtain exact solutions of solitary waves for the conformable fractional
Sharma-Tasso-Olver (STO) equation which plays an important role in nuclear physics to …

This article introduces a new iterative transform method and homotopy perturbation
transform method along with a natural transform to analyze the multi-dimensional Navier …

In this paper, we investigate the semi-analytical solution of Kaup-Kupershmidt equations
with the help of a modified method known as the new iteration transformation technique …

The Kuralay-II system (K-IIS) plays a pivotal role in modeling sophisticated nonlinear wave
processes, particularly in the field of optics. This study introduces novel soliton solutions for …

In the current study, fractional Navier–Stokes and coupled fractional Navier–Stokes
equations in various dimensions are approximated semi-analytically. In this study, the Yang …