Exploring families of soliton solutions for the fractional Akbota equation in optical fiber telecommunication systems

This work examined new analytical soliton solutions of the conformable fractional nonlinear (1+1)-dimensional Akbota problem utilizing the modified extended direct algebraic technique and a new Kudryashov method. This study investigated the application of the fractional Akbota equation in optical fiber telecommunications, where soliton solutions are crucial for maintaining signal integrity over long distances. Akbota is an integrable equation of the Heisenberg ferromagnetic variety, and it holds considerable importance for surface geometry and curve analysis in optics and magnetism. The derived soliton solutions might be characterized as dark, bright, periodic, or in other forms. The results collected are validated and shown in three-dimensional and two-dimensional graphs. The utilization of fractional derivatives has yielded results that are more contemporary than those presently found in the literature. The findings indicate that the fractional variant of the Akbota equation enhances modeling precision for nonlinear phenomena in optical fibers, rendering it an essential instrument for improving fiber optic networks. Consequently, the derived answers are beneficial for subsequent investigations of this model. The utilized methodologies yield a variety of solutions. In conclusion, the applied techniques are straightforward, effective, and dependable for solving other different models in mathematical physics. The novelty of this work lies in the application of the conformable fractional approach to the Akbota equation system, along with the implementation of new analytical methods that reveal a broader spectrum of soliton solutions, including bright, dark, periodic-singular, and breather structures, many of which have not been previously reported for this model.