Abstract
Noether theorem is an important aspect to study in dynamical systems. Noether symmetry and conserved quantity for the fractional Birkhoffian system are investigated. Firstly, fractional Pfaff actions and fractional Birkhoff equations in terms of combined Riemann-Liouville derivative, Riesz-Riemann-Liouville derivative, combined Caputo derivative and Riesz-Caputo derivative are reviewed. Secondly, the criteria of Noether symmetry within combined Riemann-Liouville derivative, Riesz-Riemann-Liouville derivative, combined Caputo derivative and Riesz-Caputo derivative are presented for the fractional Birkhoffian system, respectively. Thirdly, four corresponding conserved quantities are obtained. The classical Noether identity and conserved quantity are special cases of this paper. Finally, four fractional models, such as the fractional Whittaker model, the fractional Lotka biochemical oscillator model, the fractional Hénon-Heiles model and the fractional Hojman-Urrutia model are discussed as examples to illustrate the results.
Acknowledgements
This work is supported by the National Natural Science Foundation of China (Grant No. 11272227 and 11572212) and the Innovation Program for postgraduate in Higher Education Institutions of Jiangsu Province (KYLX 15_0405).
References
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© 2018 Diogenes Co., Sofia
Artikel in diesem Heft
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Artikel in diesem Heft
- Frontmatter
- Editorial
- FCAA related news, events and books (FCAA–volume 21–2–2018)
- Research Paper
- Initial-boundary value problems for fractional diffusion equations with time-dependent coefficients
- Research Paper
- Analytical solutions for multi-term time-space fractional partial differential equations with nonlocal damping terms
- Research Paper
- Fractional generalizations of Zakai equation and some solution methods
- Research Paper
- Stability analysis of impulsive fractional difference equations
- Research Paper
- Mellin convolutions, statistical distributions and fractional calculus
- Research Paper
- Fractional wavelet frames in L2(ℝ)
- Research Paper
- Existence of solutions for a system of fractional differential equations with coupled nonlocal boundary conditions
- Research Paper
- Two point fractional boundary value problems with a fractional boundary condition
- Research Paper
- Large deviation principle for a space-time fractional stochastic heat equation with fractional noise
- Research Paper
- Extension of Mikhlin multiplier theorem to fractional derivatives and stable processes
- Research Paper
- Noether symmetry and conserved quantity for fractional Birkhoffian mechanics and its applications
- Research Paper
- Asymptotic behavior of mild solutions for nonlinear fractional difference equations
- Research Paper
- Positive solutions to nonlinear systems involving fully nonlinear fractional operators