Purpose

The purpose of this paper is the coupled nonlinear fractal Schrödinger system is defined by using fractal derivative, and its variational principle is constructed by the fractal semi-inverse method. The approximate analytical solution of the coupled nonlinear fractal Schrödinger system is obtained by the fractal variational iteration transform method based on the proposed variational theory and fractal two-scales transform method. Finally, an example illustrates the proposed method is efficient to deal with complex nonlinear fractal systems.

Design/methodology/approach

The coupled nonlinear fractal Schrödinger system is described by using the fractal derivative, and its fractal variational principle is obtained by the fractal semi-inverse method. A novel approach is proposed to solve the fractal model based on the variational theory.

Findings

The fractal variational iteration transform method is an excellent method to solve the fractal differential equation system.

Originality/value

The author first presents the fractal variational iteration transform method to find the approximate analytical solution for fractal differential equation system. The example illustrates the accuracy and efficiency of the proposed approach.

中文翻译：

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耦合非线性分形薛定谔系统的新变分理论

目的

本文的目的是利用分形导数定义耦合非线性分形薛定谔系统，并用分形半逆方法构造其变分原理。基于所提出的变分理论和分形两尺度变换方法，通过分形变分迭代变换方法得到耦合非线性分形薛定谔系统的近似解析解。最后，一个例子说明了所提出的方法对于处理复杂的非线性分形系统是有效的。

设计/方法/方法

利用分形导数描述了耦合非线性分形薛定谔系统，并通过分形半逆方法得到了其分形变分原理。提出了一种基于变分理论求解分形模型的新方法。

发现

分形变分迭代变换法是求解分形微分方程组的一种极好的方法。

原创性/价值

作者首先提出了分形变分迭代变换方法来求分形微分方程组的近似解析解。该示例说明了所提出方法的准确性和效率。