Conformable Sumudu Transform Based Adomian Decomposition Method for Linear and Nonlinear Fractional-Order Schrödinger Equations

Abstract

Fractional-order Schrödinger differential equations extend the classical Schrödinger equation by incorporating fractional calculus to describe more complex physical phenomena. In the literature, the Schr ̈odinger 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 Schrödinger 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
Schr ̈odinger equations. Furthermore, we can conclude that the conformable fractional derivative serves as a suitable substitute for the Caputo derivative in modeling Schrödinger equations.