Abstract

The aim of this study is to establish the solution of the time-space fractional Schrödinger equation subject to initial and boundary conditions which has many applications in science such as nonlinear optics, plasma physics, super conductivity, based on the residual power series method (RPSM). We first apply suitable transformations to make the order of one of the fractional derivatives integer to implement the RPSM easily to construct the fractional power series solution. The method proposed in this article gives highly encouraging results. Illustrative examples show that this method is compatible with solving such fractional differential equations.

中文翻译：

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时空分数薛定ding方程解的新方法

摘要

这项研究的目的是建立基于初始和边界条件的时空分数Schrödinger方程的解决方案，该解决方案基于残差幂级数方法（RPSM）在非线性光学，等离子物理学，超导电性等科学领域具有许多应用）。我们首先应用适当的转换，使小数导数之一的阶数为整数，以轻松实现RPSM来构建小数幂级数解。本文提出的方法给出了令人鼓舞的结果。说明性示例表明，该方法与求解此类分数阶微分方程兼容。