Numerical investigation of two-dimensional fractional Helmholtz equation using Aboodh transform scheme

Abstract

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.

Citation

Nadeem, M., Sharaf, M. and Mahamad, S. (2024), "Numerical investigation of two-dimensional fractional Helmholtz equation using Aboodh transform scheme", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 34 No. 12, pp. 4520-4534. https://doi.org/10.1108/HFF-07-2024-0543