| Summary: | In this paper, we use the modified exponential function method in terms of Kf(x) instead of ef(x)and the extended sinh-Gordon method to find some new family solution of the M-fractional paraxial non-linear Schrödinger equation. The novel complex and real optical soliton solutions are plotted in 2-D, 3-D with a contour plot. Moreover, the dark exact solutions, singular soliton solutions, kink-type soliton solution, and periodic dark-singular soliton solutions for M-fractional paraxial non-linear Schrödinger equation are constructed. We guarantee that all solutions are new and verified the main equation of the M-fractional paraxial wave equation. For existence, the constraint condition is also added.
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