Einstein-Smoluchowsky equation handled by complex fractional moments

Author

Alotta, Gioacchino ; Di Paola, Mario

Author_Institution

Dipt. di Ing. Civile, Ambientale, Aerospaziale, dei Mater., Univ. degli Studi di Palermo, Palermo, Italy

fYear

2014

fDate

23-25 June 2014

Firstpage

1

Lastpage

6

Abstract

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.

Keywords

differential equations; diffusion; mathematical operators; method of moments; oscillators; statistical distributions; stochastic processes; transforms; Einstein-Smoluchowsky equation; Mellin transform operator; Riesz fractional derivative; alpha-stable white noise; complex fractional moments; nonlinear function; nonlinear half oscillator; probability density function; stability index; stochastic differential equation; Differential equations; Equations; Mathematical model; Probability density function; Strips; Transforms; White noise; α-stable white noise; Complex fractional moments; Einstein-Smoluchowsky equation; Nonlinear systems;

fLanguage

English

Publisher

ieee

Conference_Titel

Fractional Differentiation and Its Applications (ICFDA), 2014 International Conference on

Conference_Location

Catania

Type

conf

DOI

10.1109/ICFDA.2014.6967405

Filename

6967405