Purpose

This paper aims to present a numerical investigation for two-dimensional fractional Helmholtz equation using the Aboodh integral homotopy perturbation transform scheme (AIHPTS).

Design/methodology/approach

The proposed scheme combines the Aboodh integral transform and the homotopy perturbation scheme (HPS). This strategy is based on an updated form of Taylor’s series that yields a convergent series solution. This study analyzes the fractional derivatives in the context of Caputo.

Findings

This study illustrates two numerical examples and calculates their approximate results using AIHPTS. The derived findings are also presented in tabular form and graphical representations.

Research limitations/implications

In addition, He’s polynomials are calculated using HPS, so the minimal computational outcome is a defining feature of this method and gives a competitive advantage over other series solution techniques.

Originality/value

Numerical data and graphical illustrations for different fractional order levels confirm the proposed method’s successful performance. The results show that the proposed approach is speedy and straightforward to execute on fractional-ordered models.

中文翻译：

---

基于 Aboodh 变换方案的二维分数阶亥姆霍兹方程的数值研究

 目的

本文旨在使用 Aboodh 积分同伦扰动变换方案 （AIHPTS） 对二维分数阶亥姆霍兹方程进行数值研究。

设计/方法/方法

所提出的方案结合了 Aboodh 积分变换和同伦扰动方案 （HPS）。此策略基于 Taylor 级数的更新形式，该形式产生收敛级数解。本研究在 Caputo 的背景下分析了分数阶导数。

 发现

本研究说明了两个数值示例，并使用 AIHPTS 计算了它们的近似结果。得出的调查结果也以表格形式和图形表示形式呈现。

研究局限性/影响

此外，He 多项式是使用 HPS 计算的，因此最小计算结果是该方法的一个决定性特征，与其他级数求解技术相比具有竞争优势。

 原创性/价值

不同分数阶级别的数值数据和图形说明证实了所提出的方法的成功性能。结果表明，所提出的方法在分数阶模型上执行起来既快速又直接。