| Overview |
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1 | (8) |
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9 | (30) |
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1.1 Self-similar structures |
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9 | (3) |
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1.2 Self-similar processes |
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12 | (2) |
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1.3 Generalized (Levy) statistics |
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14 | (9) |
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1.4 Fractional Brownian motion |
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23 | (5) |
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1.5 Bifractional equation and random walks |
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28 | (8) |
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1.6 Tempered fractional processes |
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36 | (3) |
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2 Nonlocal diffusion models in hydrodynamics |
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39 | (22) |
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2.1 The Navier-Stokes equation |
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39 | (1) |
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2.2 Einstein's diffusion equation |
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40 | (3) |
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2.3 Ballistic correlations |
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43 | (4) |
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2.4 The Schonfeld eddy interpretation |
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47 | (4) |
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51 | (4) |
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2.6 The Heisenberg-Kolmogorov-Weizsacker formalism |
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55 | (3) |
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2.7 Tchen's interpretation |
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58 | (3) |
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61 | (30) |
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61 | (5) |
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3.2 Physics of anomalous diffusion |
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66 | (4) |
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3.3 Walking magnetic field lines |
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70 | (3) |
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3.4 Diffusion in molecular clouds |
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73 | (5) |
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3.5 Fractional diffusion in plasma |
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78 | (4) |
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3.6 Radio-signals from pulsars |
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82 | (5) |
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3.7 Astrophotography and image processing |
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87 | (4) |
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91 | (28) |
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4.1 Subdiffusion in photosphere |
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91 | (4) |
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4.2 Diffusion on a granular surface |
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95 | (6) |
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4.3 Solar flares and solar wind |
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101 | (4) |
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105 | (6) |
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4.5 Tempered superdiffusion parallel to magnetic field |
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111 | (8) |
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5 From classic to fractional models of cosmic ray transport |
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119 | (50) |
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5.1 Ginzburg-Syrovatsky model |
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119 | (5) |
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5.2 Collisionless Vlasov equation |
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124 | (4) |
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5.3 Cosmic rays in turbulent magnetic field |
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128 | (7) |
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5.4 Appearance of fractional derivatives in CR phenomenology |
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135 | (7) |
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5.5 Nonlocal diffusion model: physical basement |
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142 | (22) |
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5.6 Percolation of cosmic rays |
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164 | (5) |
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6 Acceleration of cosmic rays |
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169 | (20) |
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6.1 Acceleration mechanisms |
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169 | (4) |
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6.2 Two kinds of momentum diffusion operator |
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173 | (3) |
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6.3 Superdiffusive shock acceleration |
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176 | (3) |
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6.4 Subdiffusive shock acceleration |
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179 | (1) |
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6.5 Anomalous second order Fermi acceleration |
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180 | (7) |
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6.6 Stochastic acceleration in Earth's magnetotail |
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187 | (2) |
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7 Nonlocal relativistic diffusion model |
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189 | (44) |
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7.1 Relativistic speed-limit requirement and CR transport |
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189 | (5) |
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194 | (8) |
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7.3 One-dimensional NoRD theory |
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202 | (9) |
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7.4 On the energy spectrum |
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211 | (7) |
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7.5 Cosmic ray anisotropy |
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218 | (6) |
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7.6 Milne problem for a fractal half-space |
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224 | (9) |
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233 | (20) |
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8.1 Two kinds of large-scale statistics |
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233 | (3) |
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8.2 Correlation functions and power spectra |
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236 | (5) |
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8.3 Fractional Ornstein-Zernike equation |
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241 | (3) |
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8.4 Pencil beam processes |
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244 | (2) |
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8.5 The large-scale structure formation |
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246 | (7) |
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9 Conclusion: Invitation to fractional cosmology |
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253 | (12) |
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9.1 Fractional methodology |
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253 | (2) |
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255 | (1) |
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9.3 Fractional burgulence |
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256 | (2) |
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9.4 Visible subsystem as an open system |
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258 | (6) |
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9.5 Complexity and fractionality |
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264 | (1) |
| Bibliography |
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265 | |
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