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International Journal of Differential Equations
Volume 2010 (2010), Article ID 197020, 12 pages
Linear Fractionally Damped Oscillator
Department of Mathematics, Monroe County Community College, Monroe, MI 48161-9746, USA
Received 8 July 2009; Accepted 11 August 2009
Academic Editor: Mark M. Meerschaert
Copyright © 2010 Mark Naber. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Citations to this Article [15 citations]
The following is the list of published articles that have cited the current article.
- Zh Wang ZaiHua, and Hy Hu HaiYan, “Stability of a linear oscillator with damping force of the fractional-order derivative,” Science China-Physics Mechanics & Astronomy, vol. 53, no. 2, pp. 345–352, 2010.
- R. H. Rand, S. M. Sah, and M. K. Suchorsky, “Fractional Mathieu equation,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 11, pp. 3254–3262, 2010.
- F.O. Akinpelu, “The Nonlinear Fractonally Oscillator with Strong Quadratic Damping Force,” Research Journal of Applied Sciences, vol. 6, no. 7, pp. 398–404, 2011.
- Muhammad Asif Zahoor Raja, Junaid Ali Khan, and Ijaz Mansoor Qureshi, “Solution of Fractional Order System of Bagley-Torvik Equation Using Evolutionary Computational Intelligence,” Mathematical Problems in Engineering, vol. 2011, pp. 1–18, 2011.
- Wang, and Du, “Asymptotical behavior of the solution of a SDOF linear fractionally damped vibration system,” Shock and Vibration, vol. 18, no. 1-2, pp. 257–268, 2011.
- M. K. Suchorsky, and R. H. Rand, “A pair of van der Pol oscillators coupled by fractional derivatives,” Nonlinear Dynamics, vol. 69, no. 1-2, pp. 313–324, 2012.
- Ivana Kovacic, and Miodrag Zukovic, “Oscillators with a power-form restoring force and fractional derivative damping: Application of averaging,” Mechanics Research Communications, vol. 41, pp. 37–43, 2012.
- A. Y. T. Leung, Zhongjin Guo, and H. X. Yang, “Transition Curves And Bifurcations Of A Class Of Fractional Mathieu-Type Equations,” International Journal Of Bifurcation And Chaos, vol. 22, no. 11, 2012.
- Mokhtar Kirane, Milan Medved', and Nasser-eddine Tatar, “On the nonexistence of blowing-up solutions to a fractional functional-differential equation,” Georgian Mathematical Journal, vol. 19, no. 1, pp. 127–144, 2012.
- Carlos Lizama, and Gaston M. N'Guérékata, “Mild solutions for abstract fractional differential equations,” Applicable Analysis, vol. 92, no. 8, pp. 1731–1754, 2013.
- A. G. Butkovskii, S. S. Postnov, and E. A. Postnova, “Fractional integro-differential calculus and its control-theoretical applications. II. Fractional dynamic systems: Modeling and hardware implementation,” Automation and Remote Control, vol. 74, no. 5, pp. 725–749, 2013.
- José Gómez-Aguilar, Huitzilin Yépez-Martínez, Celia Calderón-Ramón, Irene Cruz-Orduña, Ricardo Escobar-Jiménez, and Victor Olivares-Peregrino, “Modeling of a Mass-Spring-Damper System by Fractional Derivatives with and without a Singular Kernel,” Entropy, vol. 17, no. 9, pp. 6289–6303, 2015.
- Li-Li Liu, and Jun-Sheng Duan, “A detailed analysis for the fundamental solution of fractional vibration equation,” Open Mathematics, vol. 13, no. 1, 2015.
- Qi Xu, Min Shi, and Zaihua Wang, “Stability and delay sensitivity of neutral fractional-delay systems,” Chaos: An Interdisciplinary Journal of Nonlinear Science, vol. 26, no. 8, pp. 084301, 2016.
- S. Saha Ray, S. Sahoo, and S. Das, “Formulation and solutions of fractional continuously variable order mass-spring-damper systems controlled by viscoelastic and viscous-viscoelastic dam,” Advances In Mechanical Engineering, vol. 8, no. 5, 2016.