Project dates: 01/01/2010 - Ongoing
A fractional operator accounts for the memory effects that are connected with many complex systems. The anomalous subdiffusion equation, fractional reaction-subdiffusion equation, fractional Stokes problem, modified subdiffusion equation, fractional Cable equation have been used to model anomalous transport in the biological cell, electrodiffusion of ions in neurons, neural cell adhesion molecules. We have proposed many effective new numerical methods and new analysis techniques for anomalous diffusion. Fractional models provide new insights into further investigations of tissue structures and the microenvironment.
Chief Investigators
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Publications
- F. Liu*, P. Zhuang, I. Turner, V. Anh and K. Burrage (2015) A semi-alternating direction method for a 2-D fractional FitzHugh-Nagumo monodomain model on an approximate irregular domain. J. Comp Physics
- F. Liu*, I. Turner and K. Burrage (2015) Computationally efficient numerical techniques for a space-fractional FitzHugh-Nagumo monodomain model. ICCES15, Tech. Science Press, (2015)
- Liu, Fawang, Turner, Ian, Anh, Vo, Yang, Qianqian, Burrage, Kevin (2013) A numerical method for the fractional Fitzhugh–Nagumo monodomain model. The ANZIAM Journal, 54, pp.C608-C629.
- Liu, Fawang, Burrage, Kevin, Hamilton, Nicholas (2013) Some novel techniques of parameter estimation for the dynamical models in biological systems. IMA Journal of Applied Mathematics, 78 (2), pp.235-260.
- Liu, Fawang, Burrage, Kevin (2011) Novel techniques in parameter estimation for fractional dynamical models arising from biological systems. Computers and Mathematics with Applications, 62 (3), pp.822-833.
- Liu, Fawang, Burrage, Kevin (2010) Parameter estimation for fractional dynamical models in biological systems. In Chen, Podlubny, I, Vinagre Jara, B M, Feliu Batlle, V, Tejado Balsera, I (Eds.), Proceedings of the 4th IFAC Workshop on Fractional Differentiation and Its Applications, pp.1-8.
