Analytical approach to study weakly nonlocal fractional Schrödinger equation via novel transform

Our main goal is to examined weakly nonlocal Schrödinger equation incorporating nonlinearity of the parabolic law and external potential using the Shehu transform decomposition method. The proposed method contributes the exact and analytical solutions for the bright soliton, dark soliton, and exponential solutions. The simulated outcomes reveal that only a few number of terms are required to achieve accurate and trustworthy approximations. Additionally, the physical behaviour of STDM solutions have been illustrated in plots for various fractional orders, and the numerical outcomes are also exhibited.