Efficient solutions for fractional Tsunami shallow-water mathematical model: A comparative study via semi analytical techniques

Abstract

In this study, we delve into the effective solution of the fractional tsunami shallow-water mathematical model. Tsunami propagation and inundation modeling is of paramount importance for hazard assessment and disaster preparedness. By employing two distinct semi-analytical techniques: the residual power series method and the modified Taylor series method, we obtain approximate solutions for the tsunami mathematical model. Solutions for varying coastal inclinations and ocean depths have been acquired for the given model taking into consideration the changes in coastal gradient and ocean depth and how to impact tsunami wave velocity and wave amplification at different values of the fractional order derivative and different steps of time. The utilized semi analytical techniques generate the solution in the form of power series expansion, so the convergence study is implemented. In order to prove the efficiency of the proposed methods, several tables for comparisons between our results and other numerical results from literature are presented. Also graphs of the obtained solutions introduced in two and three dimensions.