6533b7d9fe1ef96bd126d62a
RESEARCH PRODUCT
EXACT SOLUTIONS FOR A CLASS OF FRACTAL TIME RANDOM WALKS
Rudolf HilferRudolf Hilfersubject
Mellin transformApplied MathematicsGaussianMathematical analysisRandom walksymbols.namesakeFractalModeling and SimulationTime derivativeMaster equationsymbolsGeometry and TopologyLimit (mathematics)Critical exponentMathematicsdescription
Fractal time random walks with generalized Mittag-Leffler functions as waiting time densities are studied. This class of fractal time processes is characterized by a dynamical critical exponent 0<ω≤1, and is equivalently described by a fractional master equation with time derivative of noninteger order ω. Exact Greens functions corresponding to fractional diffusion are obtained using Mellin transform techniques. The Greens functions are expressible in terms of general H-functions. For ω<1 they are singular at the origin and exhibit a stretched Gaussian form at infinity. Changing the order ω interpolates smoothly between ordinary diffusion ω=1 and completely localized behavior in the ω→0 limit.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1995-03-01 | Fractals |