Optical soliton solutions of fractional Sasa-Satsuma equation with beta and conformable derivatives

In this paper, the optical soliton and other solutions of fractional Sasa-Satsuma equation are investigated with fractional beta derivative and conformable derivative. This model governs the interaction and propagation of the ultrashort pulses in the sub-picosecond or femtosecond regime as well as the propagation of femtosecond pulses in optical fibers. Finding optical soliton pulses or molecules to the model is essential for this reason. In this work, the fractional Sasa-Satsuma equation is investigated using the extended sinh-Gordon equation expansion method for the first time along with the two definitions of fractional derivative. The exact closed form solutions of the considered model are determined which include hyperbolic and trigonometric function solutions. Three dimensional graphs of the obtained solutions have been plotted for different values of fractional parameter. The corresponding two dimensional line graphs have also been included to illustrate the evolution of wave profile for increase in the value of fractional parameter. The obtained results show that both beta and conformal derivatives provide useful results for the fractional Sasa-Satsuma equation.