Conformable Sumudu Transform Based Adomian Decomposition Method for Linear and Nonlinear Fractional-Order Schro<spacing diaeresis>dinger Equations

Fractional-order Schro<spacing diaeresis>dinger differential equations extend the classical Schro<spacing diaeresis>dinger equation by incorporating fractional calculus to describe more complex physical phenomena. In the literature, the Schro<spacing diaeresis>dinger equation is mostly solved using fractional derivatives expressed through the Caputo derivative. However, there is limited research on exact and approximate solutions involving conformable fractional derivatives. This study aims to fill this gap by employing a hybrid approach that combines the Sumudu transform with the decomposition technique to solve the Schro<spacing diaeresis>dinger equation with conformable fractional derivatives, considering zero and nonzero trapping potentials. The efficiency of this approach is evaluated through the analysis of relative and absolute errors, confirming its accuracy. Moreover, the obtained results are compared with other techniques, including the homotopy analysis method (HAM) and the residual power series method (RPSM). The comparison demonstrates strong consistency with these methods, suggesting that our approach is a viable alternative to Caputo derivative-based methods for solving time-fractional Schro<spacing diaeresis>dinger equations. Furthermore, we can conclude that the conformable fractional derivative serves as a suitable substitute for the Caputo derivative in modeling Schro<spacing diaeresis>dinger equations.