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On the families of fractional dynamical models.
- Source :
-
Acta Mechanica . Nov2017, Vol. 228 Issue 11, p3741-3754. 14p. - Publication Year :
- 2017
-
Abstract
- In this paper, we reveal the uncertainty and its fractional generalized Hamiltonian representation for the fractional and nonlinear problem and find general methods of constructing a family of fractional dynamical models. By using the definition of combined fractional derivative, we construct a unified fractional generalized Hamiltonian equation, a fractional generalized Hamiltonian equation with combined Riemann-Liouville derivative, and a fractional generalized Hamiltonian equation with combined Caputo derivative; also, as special cases, under the different definitions of fractional derivatives, we, respectively, obtain a series of different kinds of fractional generalized Hamiltonian equations. In particular, we present a new concept of the family of fractional dynamical models, and it is found that, using the fractional generalized Hamiltonian method, we can construct a series of families of fractional dynamical models. And then, as the new method's application, we construct three new kinds of families of fractional dynamical models, which include a family of fractional Lorentz-Dirac models, a family of fractional Lotka-Volterra models and a family of fractional Hénon-Heiles models. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00015970
- Volume :
- 228
- Issue :
- 11
- Database :
- Academic Search Index
- Journal :
- Acta Mechanica
- Publication Type :
- Academic Journal
- Accession number :
- 125924072
- Full Text :
- https://doi.org/10.1007/s00707-017-1909-1