Abstract: In this study, two important fractional wave equations that describe nonlinear dispersion behaviors in complex media, namely the fractional Schrödinger equation and the complex modified Korteweg–de Vries equation, are considered. In order to model the memory effects in wave propagation more realistically, the Caputo-type fractional derivative is used. Analytical solutions are obtained by the sub-equation method based on the Riccati equation. These solutions are expressed in the form of hyperbolic, trigonometric, and rational functions. In order to reveal the effect of fractional order on wave dynamics, the real and imaginary components of the solutions are visualized in three dimensions for various parameter values. The obtained results improve the analytical understanding of fractional nonlinear systems and make a significant contribution to the current research in the field of complex wave theory.

Keywords: Fractional Schrödinger equation, fractional cmKdV equation, Sub-equation method

Pages: 512-518