Click here to view fulltext PDF

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

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

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.

MADHURI PATIL¹ SACHIN BHALEKAR^{1 2}

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

Published

8 July 2020

Manuscript received

18 December 2019

Manuscript revised

7 February 2020

Accepted

5 March 2020