In this paper, an effective analytical scheme based on Sumudu transform known as homotopy perturbation Sumudu transform method (HPSTM) is employed to find numerical solutions of time fractional Schrödinger equations with harmonic oscillator.These nonlinear time fractional Schrödinger equations describe the various phenomena in physics such as motion of quantum oscillator, lattice vibration, propagation of electromagnetic waves, fluid flow, etc. The main objective of this study is to show the effectiveness of HPSTM, which do not require small parameters and avoid linearization and physically unrealistic assumptions. The results reveal that proposed scheme is a powerful tool for study large class of problems. This study shows that the results obtained by the HPSTM are accurate and effective for analysis the nonlinear behaviour of complex systems and efficient over other available analytical schemes.

中文翻译：

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带谐振子的分数阶非线性薛定谔方程的解析研究

在本文中，一种基于 Sumudu 变换的有效解析方案，即同伦微扰 Sumudu 变换方法 (HPSTM) 被用来寻找具有谐振子的时间分数阶薛定谔方程的数值解。这些非线性时间分数阶薛定谔方程描述了物理学中的各种现象，例如如量子振荡器的运动、晶格振动、电磁波的传播、流体流动等。本研究的主要目的是展示 HPSTM 的有效性，它不需要小参数并避免线性化和物理上不切实际的假设。结果表明，所提出的方案是研究大类问题的有力工具。