Analysis of fractional non-linear tsunami shallow-water mathematical model with singular and non singular kernels

This article uses a fractional approach to investigate the system of tsunami wave propagation along an oceanic coastline. The tsunami wave system is considered under singular and nonsingular fractional operators. The double Laplace transform (LT) with Adomian decomposition method (ADM) is implemented to analyse this model. Some theoretical features of the considered fractional tsunami systems are explored via fixed point notions. Based on the shallow-water hypothesis, the current model has been explored. It is shown that changes in sea depth and coast slope have an impact on the tsunami wave’s speed and amplification at various time scales. From the numerical simulations it is observed that decrease in the fractional order decreases the tsunami wave velocity as well as height.