Abstract
In this paper, two available variants of the Schrödinger equation are studied. These two nonlinear models are characterized by considering two nonlinearity types, including Kerr and power-laws, and the conformable derivative. The integration method used in this manuscript is the generalized exponential rational function method, which is an efficient method for solving equations with partial derivatives. The technique introduces a wide range of analytical solutions for these specific structures that were not proposed in the previous literature. To investigate the behavioral characteristics and physical features of these solutions some 2D and 3D figures have been demonstrated. The method employed in this paper was able to inspect the analytical solutions for the considered equations without having the usual complexities in some other known analytical techniques. This property is one of the strengths of the present contribution. Further, the utilized method can be easily adopted for solving other nonlinear models arising in mathematical physics.
•Novel analytical solutions to the Schrodinger equation with conformable derivative are examined.•Kerr and power-law nonlinearity are incorporated in the model.•Several numerical simulations associated with the results have been performed.•An efficient analytical technique is employed.•The effects of the fractional-order on results are investigated.