The New Numerical Solutions of the Atangana-Baleanu Fractional Benney Equation

Abstract

This study focuses on the novel Atangana-Baleanu method employed to obtain new numerical solutions for the Benney equation with Atangana-Baleanu fractional derivatives. The Atangana-Baleanu q-Elzaki homotopy analysis transform method is used to numerically solve this equation. This paper presents an investigation of the numerical solutions obtained using this technique. Furthermore, the proposed method has been subjected to numerical simulation using Maple software, considering different fractional orders. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2026.