Mathematical analysis of time-fractional nonlinear Kuramoto-Sivashinsky equation

Qasem M. Tawhari; Qasem M. Tawhari

doi:10.3934/math.2025424

AIMS Mathematics

2025, Volume 10, Issue 4: 9237-9255. doi: 10.3934/math.2025424

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Mathematical analysis of time-fractional nonlinear Kuramoto-Sivashinsky equation

Qasem M. Tawhari ^,

Department of Mathematics, Faculty of Science, Jazan University, P.O. Box 2097, Jazan 45142, Kingdom of Saudi Arabia

Received: 03 February 2025 Revised: 09 March 2025 Accepted: 25 March 2025 Published: 22 April 2025
MSC : 34G20, 35A20, 35A22, 35R11

This research explored fractional Kuramoto-Sivashinsky equation analytical solutions through application of the residual power series transform method (RPSTM). The Caputo derivative approach served as the basis to analyze fractional systems since it offered a strong foundation for modeling intricate nonlinear processes. Researchers extended the Kuramoto-Sivashinsky equation through fractional domain application to capture anomalous behavior and memory effects since it showed practical uses in turbulence and plasma dynamics and flame propagation. The RPSTM proposed solution united residual power series method capabilities with integral transforms features to develop an accurate and efficient method for fractional nonlinear partial differential equation solutions. The method enabled accurate approximate solution acquisition while the procedure underwent complete convergence examination. This paper demonstrated the effectiveness and reliability of the developed method through numerical simulation results. The RPSTM proved itself as an effective analytical method for fractional differential problems which reveals vital information about the fractional Kuramoto-Sivashinsky equation behavior. The research added value to existing fractional calculus studies focused on nonlinear science applications.

Keywords:

residual power series transform method,
factional Kuramoto-Sivashinsky equation,
natural transform,
Caputo operator

Citation: Qasem M. Tawhari. Mathematical analysis of time-fractional nonlinear Kuramoto-Sivashinsky equation[J]. AIMS Mathematics, 2025, 10(4): 9237-9255. doi: 10.3934/math.2025424

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Abstract

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