A computationally efficient method for analyzing fractional Schrodinger equation using non-singular Kernel

Abstract

This article investigates a weakly nonlocal Schrödinger equation characterized by parabolic law nonlinearity and an external potential, utilizing the Laplace-Adomian Decomposition Method (LADM) with a non-singular kernel. The LADM combines the Laplace transform method with the Adomian decomposition method, providing both approximate and exact solutions for three different cases: bright solitons, dark solitons, and exponential solutions. We present numerical and graphical solutions for these cases, demonstrating that accurate and reliable approximations can be achieved with only a few terms. We compared the obtained solutions using the proposed technique with the q-homotopy analysis transform method to validate the accuracy of our results. The physical properties of the LADM solutions are illustrated through plots for different fractional orders, complemented by numerical results.