On solving non-homogeneous fractional differential equations of Euler type

In this paper, we investigate non-homogeneous fractional differential equations of Euler type with alpha-left Riemann-Liouville fractional derivatives. In fact, these fractional differential equations are analogs of Euler ordinary differential equations. The classical power series method is used to obtain a useful formula to compute a particular solution of these equations. This formula is explicit and easy to compute by using Maple software or by setting a computer code to get explicit particular solution. The related results are proved for Euler ordinary differential equations.