New solutions to the fractional perturbed Chen–Lee–Liu equation with a new local fractional derivative

Abstract

In this research a new fractional-order derivative is defined and applied to the fractional perturbed Chen–Lee–Liu nonlinear equation. Analytical soliton solutions are obtained by the modified $\exp (-\mathrm{\Omega }(\xi ))$-expansion function method (MEFM). Three new groups of bright soliton solutions, dark soliton solutions, periodic tan-type singular soliton solutions and rational singular soliton solutions are constructed with specific contains over the parameters of the nonlinear fractional perturbed Chen–Lee–Liu equation. Solutions are illustrated in 3D graphs, contour plots and 2D plots. Next, we compare our results with the results obtained previously for the nonlinear perturbed CCL. It is noticed that the solutions here introduced present some complex propagation features that appears for different time values in the 2D space graphs, these complex propagation phenomena are not observed in the integer-order nonlinear perturbed CCL equation or in the fractional case for other type of fractional derivatives previously introduced in the literature The fractional-order derivative here introduced will be very useful for the description of some nonlinear dissipation, nonlinear dispersion and other complex effects in optical wave phenomena.

Keywords:

• Fractional-order derivative
• fractional perturbed Chen–Lee–Liu nonlinear equation
• soliton solutions

Acknowledgments

We gratefully acknowledge to the Universidad Autónoma de la Ciudad de México for supporting and facilitating this research work. Huitzilin Yépez-Martínez acknowledge the support provided by SNI-CONACyT.

Disclosure statement

No potential conflict of interest was reported by the author(s).