THE PROSPECTIVE ANALYSIS OF THREE-DIMENSIONAL TIME-FRACTIONAL HELMHOLTZ MODEL USING A NEW ITERATIVE METHOD

Muhammad Nadeem, Omar Abu Arqub, Loredana Florentina Iambor, Mohamed Hussien and Ebraheem Alzahrani
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Muhammad Nadeem: School of Mathematics and Statistics, Qujing Normal University, Qujing 655011, P. R. China
Omar Abu Arqub: ��Department of Mathematics, Faculty of Science, Al-Balqa Applied University, Salt 19117, Jordan
Loredana Florentina Iambor: ��Department of Mathematics and Computer Science, University of Oradea, 1 University Street, 410087 Oradea, Romania
Mohamed Hussien: �Department of Chemistry, Faculty of Science, King Khalid University, P. O. Box 9004, Abha 61413, Saudi Arabia
Ebraheem Alzahrani: �Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia

FRACTALS (fractals), 2025, vol. 33, issue 04, 1-12

Abstract: This work proposes a new iterative method (NIM) for the analytical examination of a three-dimensional time fractional Helmholtz problem with the appropriate initial conditions that arise in various natural models. We examine the concept of fractional operators by the means of Caputo order. The Sumudu transform (ST) is coupled with the homotopy perturbation method (HPM) to develop the concept of NIM. We present two numerical examples of fractional order to demonstrate the effectiveness and validity of the proposed technique. This research presents the relationship between the NIM results and the actual outcomes for the 3D fractional Helmholtz model. The NIM results indicate that as the terms of the series solution increase, the solution progressively aligns with the actual solution. The computed values specifically demonstrate that the approach for addressing fractional order problems in physical models is extremely precise and simple to comprehend.

Keywords: New Iterative Method; Fractional Calculus; 3D Helmholtz Model; Convergence Analysis; Approximate Solution (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X25400699

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