6533b7defe1ef96bd1276987
RESEARCH PRODUCT
Einstein-Smoluchowsky equation handled by complex fractional moments
Gioacchino AlottaMario Di Paolasubject
Stochastic partial differential equationNonlinear systemStochastic differential equationMellin transformDifferential equationOperator (physics)Mathematical analysisProbability density functiona-stable white noise Nonlinear systems Einstein-Smoluchowsky equation Complex fractional momentsFractional calculusMathematicsdescription
In this paper the response of a non linear half oscillator driven by α-stable white noise in terms of probability density function (PDF) is investigated. The evolution of the PDF of such a system is ruled by the so called Einstein-Smoluchowsky equation involving, in the diffusive term, the Riesz fractional derivative. The solution is obtained by the use of complex fractional moments of the PDF, calculated with the aid of Mellin transform operator. It is shown that solution can be found for various values of stability index α and for any nonlinear function of the drift term in the stochastic differential equation.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2014-06-01 |