Work

Computational Study of Time-Fractional Kawahara and Modified Kawahara Equations with Caputo Derivatives Using Natural Homotopy Transform Method

Year: 2025

Type: article

Abstract: This article presents a computational analysis of approximate solutions for the time-fractional nonlinear Kawahara problem (KP) and the modified Kawahara problem (modified KP). This study utilizes the natural homotopy transform scheme (NHTS), which integrates the natural transform (NT) with the homotopy perturbation scheme (HPS). We derive the algebraic expression of nonlinear terms through the implementation of HPS. The fractional derivatives are considered in the Caputo form. Numerical results and visualizations present the practical interest and effectiveness of the fractional derivatives. The accuracy of the approximate results, coupled with their precise outcomes, emphasizes the reliability of the method. These findings demonstrate that NHTS is a robust and effective approach for solving time-fractional problems through series expansions.

Source: Fractal and Fractional

DOI: 10.3390/fractalfract9040247

Authors: Muhammad Nadeem, Loredana Florentina Iambor, Ebraheem Alzahrani, Azeem Hafiz P. Ajmal

Institutions: Qujing Normal University, University of Oradea, King Abdulaziz University, King Khalid University

Language: English

Topic: Fractional Differential Equations Solutions

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,258

OpenAlex ID: W4409458265

FWCI: 1.489

Cites: 30

Cited by: 2

Related to: 10