Fractional Propagation of Short Light Pulses in Monomode Optical Fibers: Comparison of Beta Derivative and Truncated M- Fractional Derivative

Abstract

Abstract The present study is dedicated to the computation and analysis of solitonic structures of a nonlinear Sasa-Satsuma equation that comes in handy to understand the propagation of short light pulses in the monomode fiber optics with the aid of Beta Derivative and Truncated M- fractional derivative. We employ new direct algebraic technique for nonlinear Sasa-Satsuma equation to derive novel soliton solutions. A variety of soliton solutions are retrieved in trigonometric, hyperbolic, exponential, rational forms. The vast majority of obtained solutions represent the lead of this method on other techniques. The prime advantage of considered technique over the other techniques is that it provides more diverse solutions with some free parameters. Moreover, the fractional behavior of the obtained solutions is analyzed thoroughly by using two and three dimensional graphs. Which shows that for lower fractional orders i.e $\beta=0.1$, the magnitude of truncated M-fractional derivative is greater whereas for increasing fractional orders i.e $\beta=0.7$ and $\beta=0.99$, magnitude remains same for both definitions except for a phase shift in some spatial domain that eventually vanishes and two curves coincide.