An analytical algorithm for nonlinear fractional Fornberg–Whitham equation arising in wave breaking based on a new iterative method

This work suggests a new analytical technique called the fractional homotopy analysis transform method (FHATM) for solving fractional Fornberg–Whitham equation. The fractional homotopy analysis transform method is an innovative adjustment in Laplace transform algorithm (LTA) and makes the calculation much simpler. In this paper, it can be observed that auxiliary parameter ℏ, which controls the convergence of the FHATM approximate series solutions, also can be used in predicting and calculating multiple solutions. This is basic and more qualitative difference in analysis between FHATM and other methods. The solutions obtained by proposed method indicate that the approach is easy to implement and computationally very attractive. The proposed method is illustrated by solving numerical example.