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Generalized Fokker-Planck equation for a class of stochastic dynamical systems driven by additive Gaussian and Poissonian fractional white noises of order α
| Content Provider | Scilit |
|---|---|
| Author | Jumarie, Guy |
| Copyright Year | 2008 |
| Abstract | In a first stage, the paper deals with the derivation and the solution of the equation of the probability density function of a stochastic system driven simultaneously by a fractional Gaussian white noise and a fractional Poissonian white noise both of the same order. The key is the Taylor’s series of fractional order f(x + h) = E α(hαDx α)f(x) where E α() denotes the Mittag-Leffler function, and D x α is the so-called modified Riemann-Liouville fractional derivative which removes the effects of the non-zero initial value of the function under consideration. The corresponding fractional linear partial differential equation is solved by using a suitable extension of the Lagrange’s technique involving an auxiliary set of fractional differential equations. As an example, one considers a half-oscillator of fractional order driven by a fractional Poissonian noise. |
| Related Links | http://www.degruyter.com/downloadpdf/j/phys.2008.6.issue-3/s11534-008-0090-5/s11534-008-0090-5.xml |
| Ending Page | 753 |
| Page Count | 17 |
| Starting Page | 737 |
| e-ISSN | 23915471 |
| DOI | 10.2478/s11534-008-0090-5 |
| Journal | Open Physics |
| Issue Number | 3 |
| Volume Number | 6 |
| Language | English |
| Publisher | Walter de Gruyter GmbH |
| Publisher Date | 2008-01-01 |
| Access Restriction | Open |
| Subject Keyword | Open Physics Applied Mathematics Mechanics Mittag Leffler Function Fractional Derivative Fokker Planck White Noise Gaussian White Noise Probability Density Function Partial Differential Equation Oscillations Fokker Planck Equation Journal: Open Physics, Issue- 3 |
| Content Type | Text |
| Resource Type | Article |
