A Computational Study of the Fractal–FractionalBenney Equation Using the Laplace–Adomian Methodand Neural Network Validation

Authors

  • Sadique Ahmad
  • Israr Ahmad Governoment Post Graduate Jhanzeb College
  • Zeeshan Ali Department of Information Management, National Yunlin University of Science and Technology, Douliu, Yunlin, Taiwan, R.O.C
  • Fady Hasan Mathematics and Sciences Department, Prince Sultan University, P.O. Box 66833, Riyadh 11586, Saudi Arabia
  • Nabil Mlaiki

DOI:

https://doi.org/10.29020/nybg.ejpam.v19i2.6800

Keywords:

Fractal-Fractional; Qualitative analysis; Laplace transform; Series solution; Neural network validation.

Abstract

In this research, the nonlinear Benney equation (BE) is examined in a fractal-fractional (FF) context with a power-law derivative. Qualitative and quantitative approaches are investigated. To study the qualitative aspects, the theory of functional analysis is used, and the Laplace Adomian decomposition method (LADM) is used to obtain an approximate analytical solution. The validity of the method is demonstrated in two numerical examples. The robustness and accuracy of the results obtained with LADM are further checked by employing a neural network (NN) approach with the Levenberg–Marquardt (LM) algorithm, complemented by regression statistics and error distribution. The suggested hybrid approach shows an outstanding correlation between analytic and predicted solutions and brings forth the effect of fractional and fractal parameters on the transmission of nonlinear dispersive waves. The research advances hybrid mathematical
and computational methods for modelling memory-dependent and self-similar processes and has potential applications in fluid dynamics, nonlinear optics, and the investigation of complex systems.

Author Biographies

  • Zeeshan Ali, Department of Information Management, National Yunlin University of Science and Technology, Douliu, Yunlin, Taiwan, R.O.C

    Department of Information Management, National Yunlin University of Science and Technology, Douliu, Yunlin, Taiwan, R.O.C

  • Fady Hasan, Mathematics and Sciences Department, Prince Sultan University, P.O. Box 66833, Riyadh 11586, Saudi Arabia

    Teacher in Mathematics and Sciences Department, Prince Sultan University, P.O. Box 66833, Riyadh 11586, Saudi Arabia

  • Nabil Mlaiki

    Professor in Mathematics and Sciences Department, Prince Sultan University, P.O. Box 66833, Riyadh 11586, Saudi Arabia

References

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Published

2026-07-28

Issue

Vol. 19 No. 2: (April 2026)

Section

Mathematical Modeling and Numerical Analysis

License

Copyright (c) 2026 Sadique Ahmad, Israr Ahmad, Zeeshan Ali, Fady Hasan, Nabil Mlaiki

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How to Cite

A Computational Study of the Fractal–FractionalBenney Equation Using the Laplace–Adomian Methodand Neural Network Validation. (2026). European Journal of Pure and Applied Mathematics, 19(2), 6800. https://doi.org/10.29020/nybg.ejpam.v19i2.6800