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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 C 0 D α t 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 λ of A are at the boundary of stable region i.e. |arg(λ)| = απ 2 . Further, we discuss the existence of singular points in the trajectories of such systems in a region of C viz. Region II. It is conjectured that there exists singular point in the solution trajectories if and only if λ ∈ Region II.The systems involving nonlocal operators are proved useful in modeling natural phenomena. In contrast with classical operators, these are able to model memory in the system. However, the behavior of non-local models may differ from those containing integer-order derivatives with respect to some aspects. This article focuses one of these aspects which is important in chaos theory viz. selfintersecting trajectories.

Fractional derivatives are generalization to classical integer-order derivatives. The rules which are true for classical derivative need not hold for the fractional derivatives, for example, we cannot simply add the fractional orders α and β inof order α+β, in general. In this article we discuss the details of such compositions and propose the conditions to split a linear fractional differential equation into the systems involving lower order derivatives. Further, we provide some examples, which show that the related results in the literature are sufficient but not necessary conditions.

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