Analysis of solution trajectories of fractional-order systems
Abstract
The behavior of solution trajectories usually changes if we replace the classical derivative in a system with a fractional one. In this article, we throw 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 (t1) of the trajectory X(t). In contrast with classical systems, these trajectories X and Y do not follow the same path. Further, we provide a Frenet apparatus for both trajectories in various cases and discuss their effect.
- Publication:
-
Pramana
- Pub Date:
- December 2020
- DOI:
- 10.1007/s12043-020-01951-8
- arXiv:
- arXiv:1904.08715
- Bibcode:
- 2020Prama..94...89P
- Keywords:
-
- Fractional derivative;
- Mittag-Leffler functions;
- Orthogonal transformation;
- Frenet apparatus;
- Mathematics - Dynamical Systems;
- 26A33;
- 37C99
- E-Print:
- 19 pages, 17 figures