Tsunami wave propagation model: A fractional approach

• Mathematical model of tsunami waves has been analysed by fractional approach. • This model is governed by coupled system of non-linear partial differential equations. and results are obtained by using fractional reduced differential transform method (FRDTM). • The coastal slope and sea depth effects on tsunami wave velocity and run-up height has been demonstrated. • Advantage of FRDTM is that it has no specific requirements for nonlinear operators, discretization, linearization, transformation, or perturbation. • One of the distinguishing practical features of this technique is its implementation on time-fractional order nonlinear PDEs without using discretization and linearization. This paper presents a fractional approach to study the mathematical model of tsunami wave propagation along a coastline of an ocean. Fractional Reduced Differential Transform Method (FRDTM) is used to analyze this model. The present model has been studied on the shallow-water assumption. It is represented by a time-fractional coupled system of non-linear partial differential equations. Solutions to the proposed model for different coastal slopes and ocean depths have been obtained. Effects of coast slope and sea depth variations on tsunami wave velocity and wave amplification have been demonstrated at different time levels and different orders α . The obtained results are compared with Elzaki Adomian Decomposition Method (EADM) to validate the proposed method for an order α = 1 .