Abstract
This paper uses the Hausdorff fractal derivative to convert the new Schrödinger nonlinear coupled equation into a novel fractal coupled nonlinear Schrödinger model. By applying the variational principle, a plethora of new soliton solutions are retrieved from the developed framework. The conditions of constraints are set for the presence of appropriate solitons. The 3D, 2D, and contour graphs of the reported solutions are depicted under the collection of appropriate parameter values. Moreover, it is noted that the variational principle built on the Hausdorff derivative for the proposed fractal model delivers a direct convenient and efficient mathematical tool for solving nonlinear partial differential equations in the solitary wave theory.