Fractional view investigation of the coupled Schrödinger-KdV equations with two approximate schemes

In this paper we explore the coupled fractional Schrödinger-KdV system, which is relevant in the modeling of the interaction of short dispersive waves with long nonlinear waves in a wide range of physical phenomena, such as in plasma physics and nonlinear optics. The use of fractional derivatives enables the model to reproduce the effects of memory and non-local dynamics which cannot be sufficiently captured by classical integer-order formulations. Residual power series transform Method (RPSTM) and the Iterative Transform Method (ITM) are two semi-analytical methods that are used in the context of the Mohand transform in order to obtain effective analytical approximations. The methods are systematically implemented to obtain the approximate solutions of the coupled system and the performance of this system is studied using convergence behavior and error analysis. Moreover, the effect of the fractional-order parameter on the mechanism of the system is examined, which reveals that the effects of fractional-order have a tremendous impact on the properties of the wave propagation, such as attenuation of the amplitude and the speed of the propagation. The paper also highlights the relevance of the fractional modeling in the representation of complex physical phenomena, which then forms a solid foundation of future studies in the nonlinear wave theory and the applied sciences.