Higher-order time-fractional Sasa–Satsuma equation: Various optical soliton solutions in optical fiber

Abstract

In this paper, the generalized (3+1)-dimensional nonlinear Sasa–Satsuma model with conformable fractional derivative using the new Kudryashov approach is considered to find a class of novel exact solutions in optical fibers. The acquired new solutions are extract by the hyperbolic functions and exponential function which are assorted as dark, bright, singular, mixed dark–bright, dark–bright, bell-shape, and periodic optical soliton solutions. The contour, three-dimension, two-dimension of various forms of the novel optical solutions are sketched to determine the prominence of the time-fractional generalized (3+1)-dimensional nonlinear Sasa–Satsuma model. In addition, to show the magnitude of the conformable fractional derivative the effect of the conformable fractional order derivative on a class of the new optical solutions are depicted via illustrative graphs. Finally, we found that the present technique is an accurate tool to investigate the analytic solutions of the fractional differential equations. The proposed Sasa–Satsuma model can be applied to the transmission of optical fibers’ ultra-fast pulses.