• Analysis of solution trajectories of fractional-order systems

• # Fulltext

https://www.ias.ac.in/article/fulltext/pram/094/0089

• # Keywords

Fractional derivative; Mittag–Lefﬂer functions; Orthogonal transformation; Frenet apparatus.

• # 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.

• # Author Affiliations

1. Department of Mathematics, Shivaji University, Kolhapur 416 004, India
2. School of mathematics and statistics, University of Hyderabad, Hyderabad 500 046, India

• # Pramana – Journal of Physics

Volume 96, 2022
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• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019

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