An efficient technique for fractional modified Boussinesq and approximate long wave equations

TL;DR

This paper introduces a computationally efficient method using q-homotopy analysis transform to solve fractional Boussinesq and long wave equations, with demonstrated accuracy and effectiveness through numerical examples.

Contribution

The paper presents a novel application of the q-homotopy analysis transform method for fractional wave equations, including convergence and error analysis.

Findings

The proposed scheme is highly accurate for fractional wave equations.

Numerical results confirm the method's effectiveness and simplicity.

Error analysis validates the scheme's precision.

Abstract

In this paper, an efficient technique is employed to study the modified Boussinesq and approximate long wave equations of the Caputo fractional time derivative, namely q-homotopy analysis transform method. These equations are playing a vital rule in describing the properties of shallow water waves through distinct dispersion relation. The convergence analysis and error analysis has been presented in the present investigation for the future scheme. We illustrate two examples to demonstrate the leverage and effectiveness of the proposed scheme, and the error analysis has been discussed to verify the accuracy. The numerical simulation has been conducted to ensure the exactness of the future technique. The obtained numerical and graphical results are divulge, the proposed scheme is computationally very accurate and straightforward to study and find the solution for fractional coupled nonlinear complex phenomena arised in science and technology.