Group-invariant solutions of fractional differential equations. (English) Zbl 1217.37066

Gazizov, R. K.; Kasatkin, A. A.; Lukashchuk, S. Y.

Tenreiro Machado, J. A. (ed.) et al., Nonlinear science and complexity. Based on the 2nd conference on nonlinear science and complexity, NSC ’08, Porto, Portugal, July 28–31, 2008. Berlin: Springer (ISBN 978-90-481-9883-2/hbk; 978-90-481-9884-9/ebook). 51-59 (2011).

The authors investigate symmetry analysis and its applications to constructing exact solutions on nonlinear fractional differential equations for a class by using infinitesimal transformations and the Caputo fractional derivative based on their paper [Vestn. USATU. 9, 3(21), 125–135 (2007)].
For the entire collection see [Zbl 1202.00103].

Reviewer: Chuangan Hu (Cupertino)

MSC:

37K30	Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures
34A08	Fractional ordinary differential equations and fractional differential inclusions

Keywords:

Lie transformations groups; exact solutions; nonlinear fractional differential equations; Caputo fractional derivative; the infinitesimal operator; fractional Riccati equation