Abstract
We present analytical solutions of the Fornberg-Whitham equations with the aid of two well-known methods: Adomian decomposition transform and variational iteration transform involving fractional-order derivatives with the Atangana-Baleanu-Caputo derivative. The Elzaki transformation is used in the Atangana-Baleanu-Caputo derivative to find the solution to the Fornberg-Whitham equations. Using certain exemplary situations, the proposed method's viability is assessed. Comparative analysis for both integer and fractional-order results is established. For validation, the solutions of the suggested methods are compared with the actual results available in the literature. Two examples are considered to check the accuracy and effectiveness of the proposed techniques.