ANALYSIS OF THE NONLINEAR FRACTIONAL BENNEY EQUATION WITH NON-SINGULAR DERIVATIVE

Israr Ahmad (), Zeeshan Ali, Khursheed Jamal Ansari (), Maryam Ali Alghafli () and Nabil Mlaiki ()
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Israr Ahmad: Department of Mathematics, Government Post Graduate Jahanzeb College, Swat 19130, Khyber Pakhtunkhwa, Pakistan
Zeeshan Ali: ��Department of Information Management, National Yunlin University of Science and Technology, Douliu, Yunlin 64002, Taiwan, R.O.C.
Khursheed Jamal Ansari: ��Department of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi Arabia
Maryam Ali Alghafli: �Department of Mathematics and Sciences, Prince Sultan University, P. O. Box 66833, Riyadh 11586, Saudi Arabia
Nabil Mlaiki: �Department of Mathematics and Sciences, Prince Sultan University, P. O. Box 66833, Riyadh 11586, Saudi Arabia

FRACTALS (fractals), 2025, vol. 33, issue 08, 1-12

Abstract: In this work, we introduce a new method for applying the Laplace Adomian decomposition method (LADM) to solve the Benney problem within the Atangana–Baleanu–Caputo (ABC) derivative framework. We provide a strong theoretical basis by carefully proving the existence and uniqueness of solutions. Our novel method offers a thorough solution process, which is graphically represented by a sequence of three- and two-dimensional plots that clearly depict the numerical solutions. This research also serves to provide a more holistic insight into the analytical understanding of Benney’s equation. It shows the flexibility and strength of LADM in solving complex mathematical problems, opening new avenues for future research in fluid flow, propagation of waves, and nonlinear systems.

Keywords: Benney Equation; Fractional Calculus; Qualitative Study; Laplace Transform; Approximate Solution (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X25401693

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