Lévy stable distribution and space-fractional Fokker–Planck type equation
The space-fractional Fokker–Planck type equation ∂p∂t+γ∂p∂x=-D(-Δ)α/2p(0<α⩽2) subject to the initial condition p(x,0)=δ(x) is solved in terms of Fox H functions. The solution as γ=0 expresses the Lévy stable distribution with the index α. From the properties of Fox H functions, the series represe...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2016-01-01
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| Series: | Journal of King Saud University: Science |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S1018364715000336 |
| Summary: | The space-fractional Fokker–Planck type equation ∂p∂t+γ∂p∂x=-D(-Δ)α/2p(0<α⩽2) subject to the initial condition p(x,0)=δ(x) is solved in terms of Fox H functions. The solution as γ=0 expresses the Lévy stable distribution with the index α. From the properties of Fox H functions, the series representation and asymptotic behavior for the solution are also obtained. Lévy stable distribution as 0<α<2 describes anomalous superdiffusion and its diffusion velocity is characterized by xd∝(Dt)1/α. |
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| ISSN: | 1018-3647 |