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Invariant analysis of nonlinear fractional ordinary differential equations with Riemann–Liouville fractional derivative

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Abstract

A systematic method is given to derive Lie point symmetries of nonlinear fractional ordinary differential equations and illustrate its applicability through the fractional Riccati equation and nonlinear fractional ordinary differential equation of Liénard type with Riemann–Liouville fractional derivative. Using the obtained Lie point symmetries, we construct their exact solutions wherever possible.

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Acknowledgments

The authors would like to thank anonymous referees for their valuable suggestions. One of the authors (T. Bakkyaraj) would like to thank the Council of Scientific and Industrial Research (CSIR), Government of India, New Delhi, for providing Senior Research Fellowship.

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Authors and Affiliations

  1. Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chepauk, Chennai, 600 005, Tamil Nadu, India

    T. Bakkyaraj & R. Sahadevan

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  1. T. Bakkyaraj
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  2. R. Sahadevan
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Correspondence to R. Sahadevan.

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Bakkyaraj, T., Sahadevan, R. Invariant analysis of nonlinear fractional ordinary differential equations with Riemann–Liouville fractional derivative. Nonlinear Dyn 80, 447–455 (2015). https://doi.org/10.1007/s11071-014-1881-4

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