Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

The Analysis of Fractional-Order Helmholtz Equations via a Novel Approach

Version 1 : Received: 5 March 2021 / Approved: 9 March 2021 / Online: 9 March 2021 (10:16:30 CET)

How to cite: Sunthrayuth, P.; Al-Zhour, Z.; Chu, Y. The Analysis of Fractional-Order Helmholtz Equations via a Novel Approach. Preprints 2021, 2021030256 (doi: 10.20944/preprints202103.0256.v1). Sunthrayuth, P.; Al-Zhour, Z.; Chu, Y. The Analysis of Fractional-Order Helmholtz Equations via a Novel Approach. Preprints 2021, 2021030256 (doi: 10.20944/preprints202103.0256.v1).

Abstract

This paper is related to the fractional view analysis of Helmholtz equations, using innovative analytical techniques. The fractional analysis of the proposed problems has been done in terms of Caputo-operator sense. In the current methodology, first, we applied the r-Laplace transform to the targeted problem. The iterative method is then implemented to obtain the series form solution. After using the inverse transform of the r-Laplace, the desire analytical solution is achieved. The suggested procedure is verified through specific examples of the fractional Helmholtz equations. The present method is found to be an effective technique having a closed resemblance with the actual solutions. The proposed technique has less computational cost and a higher rate of convergence. The suggested methods are therefore very useful to solve other systems of fractional order problems.

Subject Areas

New Iterative method; r-Laplace transform; Fractional-order Helmholtz equations; Caputo operator

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