Singular points in the solution trajectories of fractional order dynamical systems

Dynamical systems involving non-local derivative operators are of great importance inMathematical 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 D-C(0)t(alpha) X(t) = AX(t), where the coefficient matrix A 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 2 x 2 matrix A are at the boundary of stable region, i.e., vertical bar arg(lambda)vertical bar = alpha pi/2. Furthermore, we discuss the existence of singular points in the trajectories of such planar systems in a region of C, viz. Region II. It is conjectured that there exists a singular point in the solution trajectories if and only if lambda is an element of Region II. Published by AIP Publishing.