On the particular solution of constant coefficient fractional differential equations

•The paper presents an approach that comes directly from the formulation for integer order differential equations.•It generalises previous results.•It presents a matricial algorithm for dealing with the singular case.

The eigenfunction approach to compute the particular solution of constant coefficient ordinary differential equations is extended to the fractional case. It is shown that the exponentials are also the eigenfunctions of such equations. Solutions corresponding to products of powers and exponentials are presented. The singular case is studied and a matricial algorithm for its implementation is presented.