Some new soliton solutions of a semi-discrete fractional complex coupled dispersionless system.

In this paper, a semi-discrete fractional derivative complex coupled dispersionless system is proposed. The properties of M-fractional derivative are utilized to convert discrete M-fractional derivative system to a classical discrete differential system. Then the invariant subspace method (ISM) is utilized to find dark, bright, kink and W-shaped soliton solutions for the proposed system.