Journal of Nonlinear Mathematical Physics

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Volume 28, Issue 2, June 2021, Pages 219 - 241

On Lie Symmetry Analysis of Certain Coupled Fractional Ordinary Differential Equations

Authors
K. Sethukumarasamy1, *, P. Vijayaraju1, P. Prakash2, ORCID
1Department of Mathematics, Anna University, Chennai – 600 025, India
2Department of Mathematics, Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Coimbatore – 641 112, India
*Corresponding author. Email: mathsethu@gmail.com
Corresponding Author
K. Sethukumarasamy
Received 11 November 2020, Accepted 13 March 2021, Available Online 31 March 2021.
DOI
10.2991/jnmp.k.210315.001How to use a DOI?
Keywords
System of fractional ODEs; Lie group formalism; Laplace transform technique; Mittag-Leffler function; Exact solution
Abstract

In this article, we explain how to extend the Lie symmetry analysis method for n-coupled system of fractional ordinary differential equations in the sense of Riemann-Liouville fractional derivative. Also, we systematically investigated how to derive Lie point symmetries of scalar and coupled fractional ordinary differential equations namely (i) fractional Thomas-Fermi equation, (ii) Bagley-Torvik equation, (iii) two-coupled system of fractional quartic oscillator, (iv) fractional type coupled equation of motion and (v) fractional Lotka-Volterra ABC system.The dimensions of the symmetry algebras for the Bagley-Torvik equation and its various cases are greater than 2 and for this reason we construct optimal system of one-dimensional subalgebras. In addition, the exact solutions of the above mentioned fractional ordinary differential equations are explicitly derived wherever possible using the obtained symmetries.

Copyright
© 2021 The Authors. Published by Atlantis Press B.V.
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
28 - 2
Pages
219 - 241
Publication Date
2021/03/31
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.2991/jnmp.k.210315.001How to use a DOI?
Copyright
© 2021 The Authors. Published by Atlantis Press B.V.
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

risenwbib
TY  - JOUR
AU  - K. Sethukumarasamy
AU  - P. Vijayaraju
AU  - P. Prakash
PY  - 2021
DA  - 2021/03/31
TI  - On Lie Symmetry Analysis of Certain Coupled Fractional Ordinary Differential Equations
JO  - Journal of Nonlinear Mathematical Physics
SP  - 219
EP  - 241
VL  - 28
IS  - 2
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.k.210315.001
DO  - 10.2991/jnmp.k.210315.001
ID  - Sethukumarasamy2021
ER  -