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In this article, a generalized Drinfeld–Sokolov system, also calledsystem which describes the anomalous propagation of nonlinear surface gravity waves over horizontal seabed, is investigated. The Lie classical method is performed on the governing model. The obtained symmetries are used to reduce the model into the fractional ordinary differential equations and to derive the local conservation laws. To make the use of the reduced system, an explicit series solution is derived. Also, it is shown that the bright and singular solitons exist only for the time fractionalequation by means of a transformation. The considered system does not give rise to the dark soliton.

The time fractional D ( m,n ) system: invariant analysis, explicit solution, conservation laws and optical soliton