Diverse optical soliton solutions of two space-time fractional nonlinear evolution equations by the extended kudryashov method

Abstract

This study investigates the inclusive optical soliton solutions to the (2+1)-dimensional nonlinear time-fractional Zoomeron equation and the space-time fractional nonlinear Chen-Lee-Liu equation using the extended Kudryashov technique. The beta derivative is used to conduct the fractional terms and investigate wide-spectral soliton solutions to the considered models. The obtained solutions yield a variety of typical soliton shapes, including ant-peakon soliton, V-shaped soliton, anti-bell-shaped soliton, kink soliton, periodic soliton, singular periodic soliton for the specific value of the parameters. The three-dimensional, contour, and two-dimensional graphs of the derived solitons have been plotted to illustrate the structure, propagation, and influence of the fractional parameter. It is observed that the fractional parameter affects the amplitudes and periods of certain solitons. The precision of the acquired solutions is confirmed by reintroducing them into the original equation using Mathematica. The findings of this study indicate that the employed method has the capability of yielding compatible, creative, and useful solutions for diverse nonlinear evolution equations with fractional derivatives. This approach could introduce novel ways for unraveling other nonlinear equations and have implications in diverse sectors of nonlinear science and engineering.