Optical solutions to the time fractional Akbota equation arising in nonlinear optics via two distinct methods.

This paper investigates the optical soliton solutions of the time-fractional Akbota equation, a model arising in nonlinear optics. The generalized rational function method and the F-expansion approach are utilized to derive soliton solutions incorporating the beta-derivative. These solutions are depicted through 2D, contour, and 3D graphical representations, illustrating the temporal evolution of soliton profiles and revealing the influence of the fractional parameter β on soliton dynamics. The impact of the conformable derivative parameter and time on the optical solutions is also analyzed, emphasizing their role in shaping soliton properties. The graphical studies highlight the stability and propagation characteristics of solitons, offering valuable insights into their behavior under varying parameters. This research contributes to a deeper understanding of the Akbota equation, enhancing its application in surface geometry and aiding in the development of advanced models for optical and magnetic phenomena in nonlinear systems.