<p>The primary objective of this manuscript is to employ the Adomian decomposition method to derive approximate solutions for a specific class of space–time fractional-order wave equations with variable coefficients subject to prescribed initial conditions. This method provides a power-series representation of the solution without the need for linearization, weak-nonlinearity assumptions, or perturbation-based arguments. Moreover, the associated Adomian polynomials can be generated and evaluated efficiently using symbolic computation software such as <i>Mathematica</i> or <i>Maple</i>. The proposed approach exhibits considerable capability in the treatment of a broad range of nonlinear fractional-order models arising in mathematical physics. Owing to its simplicity, analytical transparency, and wide applicability, it constitutes an effective framework for investigating diverse nonlinear fractional problems in both mathematics and physics. The obtained analysis reveals a close correspondence between the infinite-series solutions constructed through the Adomian decomposition method and the classical solutions recovered when the fractional order is set to unity. Such agreement confirms the reliability and accuracy of the method in approximating solutions of fractional-order equations, particularly in the limiting case as the fractional order approaches one. In addition, the results indicate that the profile of the solution is strongly influenced by the fractional order, implying that the wave shape can be modulated without the introduction of extra physical parameters. These observations carry significant implications for the modeling and analysis of complex physical phenomena governed by fractional-order differential equations.</p>