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Received: 22 Oct. 2017 Revised: 19 Feb. 2018 Extended Abstract (Paper pages 185-200) Introduction During recent years, the theory of fractional calculus has gained notable attention from scientists due to its capability for describing various complicated natural phenomena. Complex processes in natural science can be described more exactly by using the theory of fractional calculus. Many anomalous and complicated phenomena in mechanics, chemistry, physics and other sciences have been mathematically modelled as fractional differential and integral equations. The fractional equations are very powerful mathematical tools to describe the inherent characteristics and hereditary properties of materials and processes. In many cases, finding analytical solutions of the fractional differential models is very difficult or sometimes impossible. In the last decade, many researchers have attempted to find and develop efficient numerical and analytical approaches for dealing with fractional differential equations. Recently, the Lie symmetry analysis has been improved and effectively used to deal with various types of nonlinear fractional partial differential equations. It is one of the most powerful techniques to investigate complicated nonlinear fractional models. In this paper, the generalized Lie symmetry approach proposed by Singla and Gupta is used for symmetry analysis of the time fractional Drinfeld-Sokolov-Wilson (DSW) system. The time fractional Drinfeld-Sokolov-Wilson (DSW) system is a challenging and anomalous physical model which describes nonlinear surface gravity waves propagating over horizontal seabed. The invariant subspace method is an efficient and powerful analytical approach for finding explicit particular solutions of nonlinear partial differential equations. Recently, the method has been developed by Gazizov et al. for fractional differential equations. Very recently, the method has been extended by Sahadevan and Prakash for solving a coupled system of time-fractional partial differential equations. In this study, the recent procedure is performed to find a set of explicit particular solutions of the time fractional Drinfeld-Sokolov-Wilson (DSW) system.

Lie symmetry Analysis and Explicit Exact Dolutions of the Time Fractional Drinfeld-Sokolov-Wilson (DSW) System