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

Hijaz Ahmad; Gamal M. Ismail; Ibrahim Alraddadi; Rasha F. El-Agamy; Mohammad  Aljanabi; Umar Farooq

doi:10.52866/ijcsm.2024.05.02.012

Authors

Hijaz Ahmad Near East University, Operational Research Center in Healthcare, TRNC Mersin 10, Nicosia 99138, Turkey https://orcid.org/0000-0002-5438-5407
Gamal M. Ismail Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah, Saudi Arabia https://orcid.org/0000-0002-9060-4371
Ibrahim Alraddadi Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah, Saudi Arabia https://orcid.org/0000-0002-0094-7937
Rasha F. El-Agamy Computer Science Department, Faculty of Science, Tanta University, Tanta, Egypt https://orcid.org/0009-0005-0519-3870
Mohammad Aljanabi Deputy Dean of Technical College,Imam Ja’afar Al-Sadiq University, Iraq https://orcid.org/0000-0002-6374-3560
Umar Farooq Department of Mathematics, Abdul Wali khan university Mardan, Pakistan https://orcid.org/0000-0002-5438-5407

DOI:

https://doi.org/10.52866/ijcsm.2024.05.02.012

Keywords:

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

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.