Analytic solutions of the generalized water wave dynamical equations based on time-space symmetric differential operator

It is well known that there is a deep connection between the symmetric and traveling wave solutions.It has been shown that all symmetric waves are traveling waves.In this paper,we establish new analytic solution collections of nonlinear conformable time-fractional water wave dynamical equation in a complex domain.For this purpose,we construct a new definition of a symmetric conformable differential operator(SCDO).The operator has a symmetric representation in the open unit disk.By using SCDO,we generalize a class of water wave dynamical equation type time-space fractional complex Ginzburg-Landau equation.The results show that the obtainable approaches are powerful,dependable and prepared to apply to all classes of complex differential equations.