Analysis of fractional‐order Schrödinger–Boussinesq and generalized Zakharov equations using efficient method

Abstract

In this paper, we find the solution for an interesting family of coupled Schrödinger equations exemplifying simulating consequences. The fractional Schrödinger–Boussinesq (FSB) and fractional generalized Zakharov (FGZ) equations are analyzed in the present framework usingfractional natural decomposition method(FNDM). The hired technique is graceful amalgamations of natural transform technique with Adomian decomposition scheme. Three different cases are considered, one with FSB equations and two cases are associated with FGZ equations with different initial conditions. To validate and illustrate the proficiency of the projected solution procedure, we analyzed the projected model in terms of fractional order. Further, we captured the nature of FNDM results for different values of fractional order in terms of the plots. The considered scheme is highly effective and structured while examining nonlinear models and which can be observed and confirmed from the obtained results. Moreover, the plots show that the hired fractional operator and algorithm can help to exemplify the more fascinating properties of the complex system associated with real‐world problems.