Singular dual systems of fractional-order differential equations

We consider both primal and dual formulations of singular autonomous systems of three different types of fractional-order differential equations. We present a comprehensive study which proves that by using the spectrum of a linear pencil, a polynomial matrix of first order, and not the fractional-order pencil of the prime system, we will receive information for all properties for both the prime and its dual system. In addition, by using this spectrum, the solutions for all systems can be obtained by using formulas without additional computational cost. Finally, we provide examples including a computational analysis in Modelica.