Journal
NONLINEAR DYNAMICS
Volume 80, Issue 1-2, Pages 281-286Publisher
SPRINGER
DOI: 10.1007/s11071-014-1867-2
Keywords
Discrete fractional calculus; Discrete anomalous diffusion; Discrete fractional partial difference equations
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Funding
- National Natural Science Foundation of China [11301257]
- Neijiang Normal University [13TD02]
- Guangxi Natural Science Foundation [2013GXNSFBA019021]
- Scientific Research Foundation of GuangXi University [XBZ120542]
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The tool of the discrete fractional calculus is introduced to discrete modeling of diffusion problem. A fractional time discretization diffusion model is presented in the Caputo-like delta's sense. The numerical formula is given in form of the equivalent summation. Then, the diffusion concentration is discussed for various fractional difference orders. The discrete fractional model is a fractionization of the classical difference equation and can be more suitable to depict the random or discrete phenomena compared with fractional partial differential equations.
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