A novelty of the fractional Biswas–Milovic equation with anti-cubic nonlinearity

In this study, novel solutions of the anti-cubic nonlinear fractional-order Biswas–Milovic equation are obtained for the first time using the Sardar sub-equation method, the new Kudryashov method, and the addendum to Kudryashov’s method. These methods have been successfully implemented, and several graphical representations have been provided to illustrate that higher-order nonlinear equations can be solved easily and efficiently. The obtained values and the comparisons made in the study provide a novel perspective on soliton solutions, giving new insights into the dynamics of the underlying physical systems, which are particularly relevant in fields such as nonlinear optics, quantum mechanics, and plasma physics. The results of this work show that the derived soliton solutions are directly applicable to modeling and enhancing pulse propagation in nonlinear optical fibers, enabling better control over signal dispersion and attenuation. In addition, these findings establish a mathematical framework for understanding nonlinear effects, which play a crucial role in energy transfer and stability in quantum mechanics and plasma physics.