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International Journal of Differential Equations
Volume 2010 (2010), Article ID 846107, 16 pages
On the Selection and Meaning of Variable Order Operators for Dynamic Modeling
School of Engineering, University of California, P.O. Box 2039, Merced, CA 95344, USA
Received 4 August 2009; Accepted 8 October 2009
Academic Editor: Nikolai Leonenko
Copyright © 2010 Lynnette E. S. Ramirez and Carlos F. M. Coimbra. 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 [12 citations]
The following is the list of published articles that have cited the current article.
- Hu Sheng, Hongguang Sun, YangQuan Chen, and TianShuang Qiu, “Synthesis of multifractional Gaussian noises based on variable-order fractional operators,” Signal Processing, vol. 91, no. 7, pp. 1645–1650, 2011.
- Teodor M. Atanackovic, and Stevan Pilipovic, “Hamilton's Principle With Variable Order Fractional Derivatives,” Fractional Calculus and Applied Analysis, vol. 14, no. 1, pp. 94–109, 2011.
- Chang-Ming Chen, F. Liu, I. Turner, V. Anh, and Y. Chen, “Numerical approximation for a variable-order nonlinear reaction–subdiffusion equation,” Numerical Algorithms, 2012.
- S. Shen, F. Liu, J. Chen, I. Turner, and V. Anh, “Numerical techniques for the variable order time fractional diffusion equation,” Applied Mathematics and Computation, vol. 218, no. 22, pp. 10861–10870, 2012.
- Rami Ahmad El-Nabulsi, “Fractional oscillators from non-standard Lagrangians and time-dependent fractional exponent,” Computational and Applied Mathematics, 2013.
- Deshun Yin, Yixin Wang, Yanqing Li, and Chen Cheng, “Variable-order fractional mean square displacement function with evolution of diffusibility,” Physica A: Statistical Mechanics and its Applications, 2013.
- Tatiana Odzijewicz, Agnieszka B. Malinowska, and Delfim F. M. Torres, “Noether’s theorem for fractional variational problems of variable order,” Central European Journal of Physics, 2013.
- A. G. Butkovskii, S. S. Postnov, and E. A. Postnova, “Fractional integro-differential calculus and its control-theoretical applications. I. Mathematical fundamentals and the problem of interpretation,” Automation and Remote Control, vol. 74, no. 4, pp. 543–574, 2013.
- H. Zhang, F. Liu, Mantha S. Phanikumar, and Mark M. Meerschaert, “A novel numerical method for the time variable fractional order mobile–immobile advection–dispersion model,” Computers & Mathematics with Applications, 2013.
- Shujun Shen, “The Numerical Simulation of Space-Time Variable Fractional Order Diffusion Equations,” Numerical Mathematics-Theory Methods and Applications, vol. 6, no. 4, pp. 571–585, 2013.
- Marko Janev, Stevan Pilipovic, and Dusan Zorica, “An expansion formula for fractional derivatives of variable order,” Central European Journal of Physics, vol. 11, no. 10, pp. 1350–1360, 2013.
- Ricardo Almeida, and Delfim F. M. Torres, “An Expansion Formula with Higher-Order Derivatives for Fractional Operators of Variable Order,” The Scientific World Journal, vol. 2013, pp. 1–11, 2013.