New optical soliton solutions for time-fractional Kudryashov's equation in optical fiber

In this paper, the new Kudryashov approach is considered to find several new exact solutions to time-fractional Kudryashov's equation which describes the propagation pulses in optical fibers. The present novel optical solutions are expressed via the exponential and hyperbolic functions which are categorized as dark-bright, dark, bright, bell-shape, wave, and singular optical soliton solutions. The two-dimension, three-dimension, and cantor graphs of the dark, bright, bell-shape, wave, and singular solutions are depicted to illustrate the magnitude of the time-fractional Kudryashov's equation choosing suitable values of physical parameters. Furthermore, the effect of the parameter of time and the conformable fractional order derivative is also presented. Finally, the new Kudryashov approach is an efficient technique to analysis the analytic solutions of the differential equations of integer and fractional orders.