A new local fractional derivative applied to the analytical solutions for the nonlinear Schrodinger equation with third-order dispersion

In this paper a new definition of a local fractional derivative of order a is introduced and applied to the study of the fractional nonlinear Schrodinger equation (FNLSE) with third-order dispersion and with Kerr and power laws of nonlinear refractive index. The analytical soliton solutions correspond to bright, dark and singular solitons obtained by different analytical methods. We found new optical soliton solutions with some constraints conditions that arise between the parameters of the NLSE. Typical behavior of the acquired solitons is depicted in some interesting simulations.