On new explicit solutions for solving Atangana conformable Biswas-Milovic equation with parabolic law nonlinearity in nonlinear optics

The goal of this paper is to obtain the new explicit solutions of the Atangana conformable (AC) fractional Biswas–Milovic (BM) equation with Parabolic law nonlinearity (PLN) which is a class of Schrödinger equation (SE) using a new methodology. This methodology, which is an extension of the direct algebraic method, provides some new solutions that are the advantage of this proposed approach. To exhibit the dynamical performance of this equation, some solutions are provided and drawn. Usage of the new extended direct algebraic method (NEDAM), it is obtained new optical solitons for the proposed model. The proposed method has a better efficiency in comparison to the existing methods and is straightforward for nonlinear evolution equations (NLEEs). Moreover, the introduced method can be programmed using Maple software to obtain new obvious solutions for Atangana conformable nonlinear evolution equations (ACNLEEs).