A novel approach to the motion equations of null Cartan curves via the compatible Hasimoto map.

In this manuscript, we try to understand the links between nonlinear equations of motion and equations attained by taking geometric differential description of Hasimoto map of null Cartan curves and some physical results. First, we obtain the equations of Hasimoto transformation occurred by applying Hasimoto map for null Cartan curves. Then, based on the Hasimoto map of null Cartan curves, we examine both Landau–Lifshitz system and visco Landau–Lifshitz system. Lastly, we portray the links of findings obtained by geometric physical issues. After all, we propose a new method, known as Khater method, to obtain solutions of fractional order differential equations. Also, these solutions are simulated by graphically using physical constructions. [ABSTRACT FROM AUTHOR]