We propose a semi-analytical approach based on Taylor’s theorem which is convenient for finding exact or at least approximate solution to the initial value problem for two-term fractional differential equations with Caputo fractional derivatives of noncommensurate orders. We focus on equations with real orders not exceeding 1. The two-term differential equation is first transformed into a two-order system and consequently to a system of recurrence relations which can be solved by computer. Approximation of the solution is given in the form of truncated fractional power series. The choice of order of the fractional power series is discussed and possible values of the order are determined with respect to orders of the equation. An example is included to demonstrate applicability of the approach to the considered problem.

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