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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.