Construction of diverse water wave structures for coupled nonlinear fractional Drinfel'd-Sokolov-Wilson model with Beta derivative and its modulus instability.

This paper aims to analyze the coupled nonlinear fractional Drinfel'd-Sokolov-Wilson (FDSW) model with beta derivative. The nonlinear FDSW equation plays an important role in describing dispersive water wave structures in mathematical physics and engineering, which is used to describe nonlinear surface gravity waves propagating over horizontal sea bed. We have applied the travelling wave transformation that converts the FDSW model to nonlinear ordinary differential equations.

Conservation laws, solitary wave solutions, and lie analysis for the nonlinear chains of atoms.

Nonlinear chains of atoms (NCA) are complex systems with rich dynamics, that influence various scientific disciplines. The lie symmetry approach is considered to analyze the NCA. The Lie symmetry method is a powerful mathematical tool for analyzing and solving differential equations with symmetries, facilitating the reduction of complexity and obtaining solutions.

An Investigation of Fractional Bagley-Torvik Equation.

In this article, we will solve the Bagley-Torvik equation by employing integral transform method. Caputo fractional derivative operator is used in the modeling of the equation. The obtained solution is expressed in terms of generalized function.