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Topics in Nonlinear Mechanics and Physics pp 203–227Cite as

Complex Fractional Moments for the Characterization of the Probabilistic Response of Non-linear Systems Subjected to White Noises

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Part of the book series: Springer Proceedings in Physics ((SPPHY,volume 228))

Abstract

In this chapter the solution of Fokker-Planck-Kolmogorov type equations is pursued with the aid of Complex Fractional Moments (CFMs). These quantities are the generalization of the well-known integer-order moments and are obtained as Mellin transform of the Probability Density Function (PDF). From this point of view, the PDF can be seen as inverse Mellin transform of the CFMs, and it can be obtained through a limited number of CFMs. These CFMs’ capability allows to solve the Fokker-Planck-Kolmogorov equation governing the evolutionary PDF of non-linear systems forced by white noise with an elegant and efficient strategy. The main difference between this new approach and the other one based on integer moments lies in the fact that CFMs do not require the closure scheme because a limited number of them is sufficient to accurately describe the evolutionary PDF and no hierarchy problem occurs.

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Authors and Affiliations

  1. Department of Engineering, University of Palermo, Viale Delle Scienze Ed. 8, 90128, Palermo, Italy

    Mario Di Paola, Antonina Pirrotta, Gioacchino Alotta & Alberto Di Matteo

  2. Department of Structures for Engineering and Architecture (DIST), University of Naples “Federico II”, Via Claudio 21, Ed. 6, 80125, Naples, Italy

    Francesco Paolo Pinnola

Authors
  1. Mario Di Paola
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  2. Antonina Pirrotta
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  3. Gioacchino Alotta
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  4. Alberto Di Matteo
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  5. Francesco Paolo Pinnola
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Corresponding author

Correspondence to Antonina Pirrotta .

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Editors and Affiliations

  1. Faculty of Sciences Ain Chock, University Hassan II - Casablanca, Casablanca, Morocco

    Mohamed Belhaq

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Di Paola, M., Pirrotta, A., Alotta, G., Di Matteo, A., Pinnola, F.P. (2019). Complex Fractional Moments for the Characterization of the Probabilistic Response of Non-linear Systems Subjected to White Noises. In: Belhaq, M. (eds) Topics in Nonlinear Mechanics and Physics. Springer Proceedings in Physics, vol 228. Springer, Singapore. https://doi.org/10.1007/978-981-13-9463-8_11

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