Local fractional q-homotopy analysis transform method (q -HATM) is employed to solve the local fractional Helmholtz equation. Uniqueness and convergence analysis of the method is investigated by Banach’s fixed point theory. Solutions are expressed in the form of rapidly series with fast computable basics by Mathematica software. Reliability analysis is provided. Computational results display that LFq-HATM is an efficient and powerful method to obtain solutions to the present equation and has the potential to be applicable to other related fractional-order systems.

中文翻译：

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局部分数亥姆霍兹方程的收敛性分析和数值解

采用局部分数q同伦分析变换方法（q -HATM）求解局部分数Helmholtz方程。该方法的唯一性和收敛性分析是通过Banach不动点理论进行的。解决方案通过Mathematica软件以具有快速可计算基础知识的快速序列的形式表示。提供了可靠性分析。计算结果表明，LFq-HATM是获得当前方程解的一种有效且强大的方法，并且有可能适用于其他相关的分数阶系统。