An Analytical Approach to Solve the Fractional Benney Equation Using the q-Homotopy Analysis Transform Method

This paper introduces an analytical approach for solving the Benney equation using the q-homotopy analysis transform method. The Benney equation is a nonlinear partial differential equation that has applications in diverse areas of physics and engineering. The q-homotopy analysis transform method is a numerical technique that has been successfully employed to solve a broad range of nonlinear problems. By utilizing this method, we derive approximate analytical solutions for the Benney equation. The results demonstrate that this method is a powerful and effective tool for obtaining accurate solutions for the equation. The proposed method offers a valuable contribution to the existing literature on the behavior of the Benney equation and provides researchers with a useful tool for solving this equation in various applications.