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Fokker Planck equation solved in terms of complex fractional moments

Mario Di Paola

subject

Mellin transformMechanical Engineeringmedia_common.quotation_subjectFokker Planck equationMathematical analysisZero (complex analysis)Aerospace EngineeringOcean EngineeringStatistical and Nonlinear PhysicsProbability density functionComplex fractional momentCondensed Matter PhysicsInfinityDomain (mathematical analysis)Fractional calculusNuclear Energy and EngineeringFokker–Planck equationFinite setMellin transformRiesz fractional integrals.Civil and Structural EngineeringMathematicsmedia_common

description

Abstract In this paper the solution of the Fokker Planck (FPK) equation in terms of (complex) fractional moments is presented. It is shown that by using concepts coming from fractional calculus, complex Mellin transform and related ones, the solution of the FPK equation in terms of a finite number of complex moments may be easily found. It is shown that the probability density function (PDF) solution of the FPK equation is restored in the whole domain, including the trend at infinity with the exception of the value of the PDF in zero.

yearjournalcountryeditionlanguage
2014-10-01Probabilistic Engineering Mechanics
https://doi.org/10.1016/j.probengmech.2014.09.003