Exploring Advanced Analysis Technique for Shallow Water Flow Models with Diverse Applications

Abstract

The present article focuses on the analytical approach using fractional orders and its application in the dynamics of physical processes. Fractional order models align better with experimental data compared to non-fractional ones. This study primarily focuses on employing the new approximate analytical method to solve shallow water models with fractional orders. Numerical examples within the Caputo fractional derivative showcase the method’s application. Results for both integer and fractional orders are graphically depicted, demonstrating the fractional solutions’ closeness to actual data. Analysis of 3D and 2D fractional order graphs reveals convergence toward integer order graphs as fractional derivatives approach non-fractional ones. This method shows promise for direct application in solving targeted problems and can be easily adapted for other fractional nature problems.

Keywords

• Water flow models, fractional view analysis, analytical solution, new approximate analytical method, Riemann-Liouuille partial fractional order operator of integration, Caputo operator.