THE FRACTIONAL ANALYSIS OF (2 + 1)-DIMENSIONAL NONLINEAR TIME-FRACTIONAL ROSENAU–HYMAN MODEL USING NATURAL HOMOTOPY TRANSFORM METHOD

Muhammad Nadeem (), Yabin Shao, Mrim M. Alnfiai, Mohamed Hussien and Salma Mohsen M. Alnefaie
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Muhammad Nadeem: School of Mathematics and Statistics, Qujing Normal University Qujing, Yunnan, 655011, P. R. China
Yabin Shao: ��Research Institute of Microscale Optoelectronics, School of Jia Yang, Zhejiang Shuren University, Shaoxing, Zhejiang, P. R. China
Mrim M. Alnfiai: ��Department of Information Technology, College of Computers and Information Technology, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia
Mohamed Hussien: �Department of Chemistry, Faculty of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia
Salma Mohsen M. Alnefaie: �Department of Physics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia

FRACTALS (fractals), 2025, vol. 33, issue 05, 1-16

Abstract: This study investigates the approximate solution of the (2 + 1)-dimensional time-fractional Rosenau–Hyman model utilizing the natural homotopy transform method (NHTM). This proposed scheme is developed by coupling the natural transform (NT) and the homotopy perturbation method (HPM). We explain the fractional derivatives of the functions using the Caputo concept. We illustrate two numerical applications and compare the obtained results with the precise results of the proposed model. We present the behaviors of the obtained results for multiple orders of derivatives in two-dimensional and three-dimensional graphical representations. The convergence of the obtained solution is validated by reducing the errors over the consecutive series for the NHTM results. Consequently, the NHTM is considered the most advanced computational scheme for the approximate results of nonlinear fractional problems.

Keywords: Natural Transform; Fractional Calculus; Convergence Analysis; Rosenau–Hyman Equation; Approximate Solution (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X25500318

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