@article{El-Ajou2024, 
author = {Ahmad El-Ajou and Rania Saadeh and Moawaih Akhu Dunia and Ahmad Qazza and Zeyad Al-Zhour},
title = {A new approach in handling one-dimensional time-fractional Schrödinger equations},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {5},
pages = {10536-10560},
keywords = {fractional operators, fractional Schrödinger equation, multiple fractional power series, Laplace residual power series method},
url = {https://www.sciopen.com/article/10.3934/math.2024515},
doi = {10.3934/math.2024515},
abstract = {Our aim of this paper was to present the accurate analytical approximate series solutions to the time-fractional Schrödinger equations via the Caputo fractional operator using the Laplace residual power series technique. Furthermore, three important and interesting applications were given, tested, and compared with four well-known methods (Adomian decomposition, homotopy perturbation, homotopy analysis, and variational iteration methods) to show that the proposed technique was simple, accurate, efficient, and applicable. When there was a pattern between the terms of the series, we could obtain the exact solutions; otherwise, we provided the approximate series solutions. Finally, graphical results were presented and analyzed. Mathematica software was used to calculate numerical and symbolic quantities.}
}