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    • Analysis of solution trajectories of fractional-order systems

      MADHURI PATIL SACHIN BHALEKAR

      Research Article Volume 94 Published: 8 July 2020 Article ID 0089

    • Fulltext

       

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      Permanent link:
      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

       

      MADHURI PATIL1 SACHIN BHALEKAR1 2

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

    • Dates

       
      Published
      8 July 2020
      Manuscript received
      18 December 2019
      Manuscript revised
      7 February 2020
      Accepted
      5 March 2020

  • Pramana – Journal of Physics | News

    • Editorial Note on Continuous Article Publication

      Posted on July 25, 2019

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