NDLI: Variational integrators for fractional Birkhoffian systems

Content Provider	SpringerLink
Author	He, Lin Wu, Huibin Mei, Fengxiang
Copyright Year	2016
Abstract	In this paper, we generalize the Pfaff–Birkhoff principle to the case of containing fractional derivatives and obtain the so-called fractional Pfaff–Birkhoff–d’Alembert principle. The fractional Birkhoff equations in the sense of Riemann–Liouville fractional derivative are derived. Under the framework of variational integrators, we develop the discrete fractional Birkhoff equations by approximating the Riemann–Liouville fractional derivative with the shifted Grünwald–Letnikov fractional derivative. The resulting algebraic equations can be served as an algorithm to numerically solve the fractional Birkhoff equations. A numerical example is demonstrated to show the validity and applicability of the presented methodology.
Starting Page	2325
Ending Page	2334
Page Count	10
File Format	PDF
ISSN	0924090X
Journal	Nonlinear Dynamics
Volume Number	87
Issue Number	4
e-ISSN	1573269X
Language	English
Publisher	Springer Netherlands
Publisher Date	2016-11-19
Publisher Place	Dordrecht
Access Restriction	Subscribed
Subject Keyword	Variational integrators Riemann–Liouville fractional derivative Fractional Pfaff–Birkhoff–d’Alembert principle Discrete fractional Birkhoff equations Vibration, Dynamical Systems, Control Classical Mechanics Mechanical Engineering Automotive Engineering
Content Type	Text
Resource Type	Article
Subject	Aerospace Engineering Applied Mathematics Control and Systems Engineering Mechanical Engineering Electrical and Electronic Engineering Ocean Engineering

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