Discrete Fractional Diffusion Equation of Chaotic Order
作者： Guo-Cheng Wu , Dumitru Baleanu , He-Ping Xie , Sheng-Da Zeng
DOI: 10.1142/S0218127416500139
关键词:
摘要: Discrete fractional calculus is suggested in diffusion modeling porous media. A variable-order equation proposed on discrete time scales. function of the variable order constructed by a chaotic map. The model shows some new random behaviors comparison with other cases.
harvard.edu
dissem.in参考文章(27)
Rudolf Gorenflo, Francesco Mainardi, Daniele Moretti, Paolo Paradisi, Time Fractional Diffusion: A Discrete Random Walk Approach Nonlinear Dynamics. ,vol. 29, pp. 129- 143 ,(2002) , 10.1023/A:1016547232119
Dorota Mozyrska, Ewa Girejko, Overview of fractional h-difference operators Advances in harmonic analysis and operator theory, 2013, ISBN 978-3-0348-0515-5, págs. 253-268. pp. 253- 268 ,(2013) , 10.1007/978-3-0348-0516-2_14
F. Liu, S. Shen, V. Anh, I. Turner, Analysis of a discrete non-Markovian random walk approximation for the time fractional diffusion equation Anziam Journal. ,vol. 46, pp. 488- 504 ,(2005) , 10.21914/ANZIAMJ.V46I0.973
Carl F. Lorenzo, Tom T. Hartley, Variable Order and Distributed Order Fractional Operators Nonlinear Dynamics. ,vol. 29, pp. 57- 98 ,(2002) , 10.1023/A:1016586905654
C.-M. Chen, F. Liu, K. Burrage, Y. Chen, Numerical methods of the variable-order Rayleigh–Stokes problem for a heated generalized second grade fluid with fractional derivative Ima Journal of Applied Mathematics. ,vol. 78, pp. 924- 944 ,(2013) , 10.1093/IMAMAT/HXR079
Ferhan M. Atici, Paul W. Eloe, Initial value problems in discrete fractional calculus Proceedings of the American Mathematical Society. ,vol. 137, pp. 981- 989 ,(2008) , 10.1090/S0002-9939-08-09626-3
S. Shen, F. Liu, J. Chen, I. Turner, V. Anh, Numerical techniques for the variable order time fractional diffusion equation Applied Mathematics and Computation. ,vol. 218, pp. 10861- 10870 ,(2012) , 10.1016/J.AMC.2012.04.047
Michael T. Holm, The Laplace transform in discrete fractional calculus Computers & Mathematics With Applications. ,vol. 62, pp. 1591- 1601 ,(2011) , 10.1016/J.CAMWA.2011.04.019
HongGuang Sun, Wen Chen, Hu Sheng, YangQuan Chen, On mean square displacement behaviors of anomalous diffusions with variable and random orders Physics Letters A. ,vol. 374, pp. 906- 910 ,(2010) , 10.1016/J.PHYSLETA.2009.12.021
F. Liu, V. V. Anh, I. Turner, P. Zhuang, Time fractional advection-dispersion equation Journal of Applied Mathematics and Computing. ,vol. 13, pp. 233- 245 ,(2003) , 10.1007/BF02936089