The causal α-exponential and the solution of fractional linear time-invariant systems

Closed-form expressions for the impulse and step responses of commensurable linear time-invariant systems are deduced and exemplified. The algorithm is based on obtaining the solution in terms of the α-exponential monomials that generate a vector space containing the solutions of such systems. Several examples are considered, together with the numerical aspects involved in calculating the related series, which show the accuracy and effectiveness of the approach.