Abstract
In this paper, we consider a new class of conformable fractional derivative for constructing new exact solitary wave solutions to the fractional perturbed nonlinear Schrodinger equation with power law nonlinearity, which describes the effects of quantic nonlinearity on the ultrashort optical solitons pulse propagation in non-Kerr media.These solitary wave solutions demonstrate the fact that solutions to the perturbed nonlinear Schrodinger equation with power law nonlinearity model can exhibit a variety of behaviors. For more illustration we consider the graphs for one of the solutions. It show that with changing \(\alpha \) (if \(\alpha \) tends to one; \(\alpha \) is fractional symbol) the graphs of the solutions of fractional perturbed nonlinear Schrodinger equation with power law nonlinearity is near to graph of solution of perturbed nonlinear Schrodinger equation with power law nonlinearity in general form.
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