This paper presents a thorough study of a time-dependent nonlinear Schrödinger (NLS) differential equation with a time-fractional derivative. The fractional time complex transform is used to convert the problem into its differential partner, and its nonlinear part is then discretized using He’s polynomials so that the homotopy perturbation method (HPM) can be applied powerfully. The two-scale concept is used to explain the substantial meaning of the fractional time complex transform and the solution.

中文翻译：

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分数阶复数变换：时间分数阶薛定谔方程的一种新方法

本文对具有时间分数导数的时间相关非线性薛定谔 (NLS) 微分方程进行了深入研究。分数次时间复数变换用于将问题转换为其微分伙伴，然后使用He多项式对其非线性部分进行离散化，从而可以有效地应用同伦摄动法（HPM）。两尺度概念用于解释分数阶时间复数变换的实质意义及解。