Analysis of solution trajectories of linear fractional order systems

Abstract

The behavior of solution trajectories usually changes if we replace the classical derivative in a system by a fractional one. In this article, we throw a light on the relation between two trajectories $X(t)$ and $Y(t)$ of such a system, where the initial point $Y(0)$ is at some point $X(t_1)$ of trajectory $X(t)$. In contrast with classical systems, trajectories $X$ and $Y$ do not follow the same path. Further, we provide a Frenet apparatus of both trajectories in various cases and discuss their effect.

19 pages, 17 figures

References in corpus (3)

• Fractional derivative models for atmospheric dispersion of pollutants
• Singular points in the solution trajectories of fractional order dynamical systems
• Can we split fractional derivative while analyzing fractional differential equations?

Cited by in corpus (1)

• Nonexistence of invariant manifolds in fractional order dynamical systems