Mamadu-Adomain Decomposition Method for Time-Fractional Wave Equation

The present study explores the Mamadu-Adomain Decomposition Method (MADM) for solving fractional wave equations. The method is formulated by coupling the Mamadu Transform and the Adomain Decomposition Methods. The Mamadu Transforms handles the non-integer order derivatives, especially those defined in the Caputo Fractional derivative. The method is an analytical-numerical approach powered by power series decomposition techniques without requiring the standard traditional discretization methods to generate accurate and reliable solutions. Numerical evidences are presented in 2D and 3D plots to show convergence. The results suggest that the MADM offers significant advantages, including reduced complexity and adaptability to initial functions. Also, the method offers a balance between analytical insight and computational feasibility.