Solving the fractional Fornberg-Whitham equation within Caputo framework using the optimal auxiliary function method

Abstract

In this work, we solve the fractional-order Fornberg-Whitham (FW) problem in the context of the Caputo operator by using the Optimal Auxiliary Function Method. Tables and figures showing full numerical findings indicate the correctness and efficacy of this strategy. The results provide insights into the solution behavior of the FW equation and demonstrate the applicability of the Optimal Auxiliary Function Method. By giving insight on the behavior of the FW equation in a fractional context, this research advances the use of fractional calculus techniques in the solution of complicated differential equations.

The exact solutions for the fractional Riemann wave equation in quantum mechanics and optics

“…The solutions of these equations yields the following two sets: For the first set, the solutions of FRWE-MTD (1), utilizing (11), are…”

“…Due to the importance of FNLEE, many authors have proposed many methods for obtaining its solutions for instance Lie symmetry method [6], Lie group analysis [7,8], fractional sub-equation method [9], invariant subspace method [8], Jacobi elliptic function method [10], optimal auxiliary function method [11], generalized Riccati equation method [12], He's semi-inverse method [13], and etc.…”