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In the present paper, we successfully solve some linear fractional differential equations (FDE) analytically by solving an auxiliary linear differential equation with an integer order. The idea of the suggested method is based on transforming the given FDE into a linear differential equation with an integer order. This transformation removes certain terms of the solution of the considered FDE, resulting in the remaining terms being a solution to the auxiliary equation. To demonstrate the ability and efficacy of this idea, several examples have been provided.