A Highly Accurate Technique to Obtain Exact Solutions to Time-Fractional Quantum Mechanics Problems with Zero and Nonzero Trapping Potential

In this study, the highly accurate analytical Aboodh transform decomposition method (ATDM) in sense of Caputo fractional derivative is used to determine approximate and exact solutions both linear nonlinear time-fractional Schrodinger differential equations (SDEs) with zero nonzero trapping potential that describe nonrelativistic quantum mechanical activity. The Adomian (ADM) Caputo’s are combined method. recurrence absolute error four problems analyzed evaluate efficiency consistency presented addition, numerical results also compared other methods such as reduced (FRDTM), homotopy analysis (HAM), perturbation (HPM). obtained by proposed show excellent agreement these methods, which indicates its effectiveness reliability. This technique has benefit not requiring any minor or major physical parameter assumptions problem. As a result, it may be solve weakly strongly problems, overcoming some inherent constraints classic approaches. To fractional-order equations, just few computations necessary. consequence, outperforms approaches significantly. procedure quick, precise, easy implement. Convergence series solution offered.