A new approach in handling one-dimensional time-fractional Schrödinger equations-Reference-Cited by-同舟云学术

A new approach in handling one-dimensional time-fractional Schrödinger equations

Published:2024 Issue:5 Volume:9 Page:10536-10560
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

El-Ajou Ahmad¹,Saadeh Rania²,Dunia Moawaih Akhu¹,Qazza Ahmad²,Al-Zhour Zeyad³

Affiliation:

1. Department of Mathematics, Faculty of Science, Al-Balqa Applied University, Salt 19117, Jordan

2. Department of Mathematics, Faculty of Science, Zarqa University, Zarqa 13110, Jordan

3. Department of Basic Engineering Sciences, College of Engineering, Imam Abdulrahman Bin Faisal University, P.O. Box 1982, Dammam 31441, Saudi Arabia

Abstract

<abstract> <p>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.</p> </abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

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