Singular points in the solution trajectories of fractional order dynamical systems

Dynamical systems involving non-local derivative operators are of great importance in Mathematical analysis and applications. This article deals with the dynamics of fractional order systems involving Caputo derivatives. We take a review of the solutions of linear dynamical systems $$ , where the coefficient matrix $$ is in canonical form. We describe exact solutions for all the cases of canonical forms and sketch phase portraits of planar systems. We discuss the behavior of the trajectories when the eigenvalues $$ of $$ matrix $$ are at the boundary of stable region, i.e., $$ . Furthermore, we discuss the existence of singular points in the trajectories of such planar systems in a region of $$ , viz. Region II. It is conjectured that there exists a singular point in the solution trajectories if and only if $$ Region II.