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 \(X(t_1)\) 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.

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Acknowledgements

Authors are thankful to the Editor and the Reviewers for their insightful comments. S Bhalekar acknowledges the Science and Engineering Research Board (SERB), New Delhi, India for the Research Grant (Ref. MTR/2017/000068) under Mathematical Research Impact Centric Support (MATRICS) Scheme. M Patil acknowledges Department of Science and Technology (DST), New Delhi, India for INSPIRE Fellowship (Code-IF170439).

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Correspondence to Sachin Bhalekar.

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Patil, M., Bhalekar, S. Analysis of solution trajectories of fractional-order systems. Pramana - J Phys 94, 89 (2020). https://doi.org/10.1007/s12043-020-01951-8

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Keywords

  • Fractional derivative
  • Mittag–Leffler functions
  • Orthogonal transformation
  • Frenet apparatus

PACS Nos

  • 05.45.–a
  • 02.40.–k
  • 45.30.+s