In this paper the response of a non linear half oscillator driven by a-stable white noise in terms of probability density function (PDF) is investigated. The evolution of the PDFof 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 Mellintransform operator. It is shown that solution can be found for various values of stability index a and for any nonlinear function f (X; t).
|Numero di pagine||6|
|Stato di pubblicazione||Published - 2014|
All Science Journal Classification (ASJC) codes
- Applied Mathematics
- Modelling and Simulation
- Numerical Analysis