Optical soliton solutions to the time-fractional Kundu–Eckhaus equation through the -expansion technique

The present research focuses on fractional nonlinear evolution equations and their optical soliton solutions, which have become the inquisitive context to study their significant attributes in understanding natural kernels ascending in the field of science and technology. This article has been dedicated to searching out the analytical soliton solution of an important fractional nonlinear evolution equation, named the time-fractional Kundu–Eckhaus equation in the sense of beta fractional derivative through the (\(G^{\prime}/G, 1/G\))-expansion approach. This equation was originated to search out the transmission of data through the optical fiber. By exerting the stated method, abundant novel soliton solutions, like kink soliton, compacton, periodic soliton, singular periodic, singular bell-shaped soliton, and others have been established. In accordance with the trail solutions generated in this method, the solutions contain arbitrary parameters and hyperbolic, rational, and trigonometric functions. Soliton solutions are extracted from analytical solutions for apposite values of the parameters. Contour, three- and two-dimensional graphs are plotted to demonstrate the physical structure and characteristics of the attained solitons. The obtained results imply that the concerned method can be used to attain diverse, improved, useful, and compatible solutions for other significant fractional nonlinear evolution equations.