An application of fractional differential equations is on the rise across physics, biology, and engineering. This is especially true when standard integer-order models fail to adequately describe a given phenomenon. A large number of practical systems rely on these equations, which enable the accounting for memory and nonlocal effects. But the mathematical complexity of high-order fractional models makes them difficult to address. To approximate solutions to these kinds of problems, this research employs the Adomian Decomposition Method in combination with the Natural Transform. The fractional derivatives are transformed to algebraic expressions using the Natural Transform, and nonlinear terms are systematically treated using the Adomian technique. This method is validated for fractional differential equations by the numerical results obtained for fractional orders between 4.7 and 4.9, which show that stable solutions with absolute errors less than one are produced.