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 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 a and for any nonlinear function f (X; t).
Alotta, G., Di Paola, M. (2014). Einstein-Smoluchowsky equation handled by complex fractional moments. In IEEE 2014, Fractional Differentiation and Its Applications (ICFDA), 2014 International Conference on [10.1109/ICFDA.2014.6967405].
Einstein-Smoluchowsky equation handled by complex fractional moments
ALOTTA, Gioacchino;DI PAOLA, Mario
2014-01-01
Abstract
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 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 a and for any nonlinear function f (X; t).
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