Search results for "Fractional integral"

showing 3 items of 3 documents

Exact mechanical models of fractional hereditary materials

2012

Fractional Viscoelasticity is referred to materials, whose constitutive law involves fractional derivatives of order β R such that 0 β 1. In this paper, two mechanical models with stress-strain relation exactly restituting fractional operators, respectively, in ranges 0 β 1 / 2 and 1 / 2 β 1 are presented. It is shown that, in the former case, the mechanical model is described by an ideal indefinite massless viscous fluid resting on a bed of independent springs (Winkler model), while, in the latter case it is a shear-type indefinite cantilever resting on a bed of independent viscous dashpots. The law of variation of all mechanical characteristics is of power-law type, strictly related to th…

Hereditary materialMechanical EngineeringMathematical analysisConstitutive equationFractional derivativeType (model theory)Viscous liquidCondensed Matter PhysicsPower lawViscoelasticityDashpotFractional calculusClassical mechanicsMechanical fractancePower-lawsMechanics of MaterialsGeneral Materials ScienceIdeal (ring theory)Settore ICAR/08 - Scienza Delle CostruzioniFractional integralMathematicsJournal of Rheology
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Fokker Planck equation solved in terms of complex fractional moments

2014

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.

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_commonProbabilistic Engineering Mechanics
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Some Inclusion Theorems for Orlicz and Musielak-Orlicz Type Spaces

1995

where K is a homogeneous kernel and f belongs to some KSthe functional space. In these papers the estimates are taken with respect to the KSthe norm of the space. Recently in [2] we obtained analogous estimates for functions belonging to Orlicz or Musielak-Orlicz type spaces L ~, with respect to the canonical modular functional. These results enable us to say that, for example,

Pure mathematicsMusielak-Orlicz spacesApplied MathematicsNorm (mathematics)Mathematical analysisFunctional spaceBirnbaum–Orlicz spaceOrlicz spacesRiemann-Liouville fractional integralHomogeneous kernelOrlicz spaces; Musielak-Orlicz spaces; Riemann-Liouville fractional integral; homogeneous kernelshomogeneous kernelsMathematics
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