Singular dual systems of fractional?order differential equations

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