Alternative Variational Iteration Elzaki Transform Method for Solving Time‐Fractional Regularized Long Wave Equation

ABSTRACT In this research work, a new algorithm is proposed, which involves coupling a new integral transform, namely, the Elzaki transform, with a well‐known alternative variational iteration method called the alternative variational iteration Elzaki transform method, to solve both linear and nonlinear time‐fractional regularized long wave equations. Six examples have been examined of regularized long‐wave equations, widely used in various applied sciences and engineering fields, including space‐charge waves, ion‐acoustic swells, ocean engineering, tsunami modeling, and plasma. The existence, uniqueness, and stability analysis of the solution demonstrated the efficiency and authenticity of the method, showing that the solutions derived from the alternative variational iteration Elzaki transform method are both convergent and unique. This method generates reliable solutions to a wider class of nonlinear partial differential equations in a simple manner, without the need for discretization, linearization, or computation of Adomian polynomials. The obtained results were validated by comparing them with exact results and results from other existing literature using tables of comparison, 3D plots, and convergence analysis.