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RESEARCH PRODUCT
Fractional Derivatives in Interval Analysis
Roberta SantoroGiulio CottoneGiulio Cottonesubject
Dynamical systems Integral equations02 engineering and technology01 natural sciencesTransfer functionInterval arithmeticStructural Uncertainty Viscoelasticity Fractional Calculus Interval Analysissymbols.namesake0203 mechanical engineeringDynamical systemsmedicine0101 mathematicsSafety Risk Reliability and QualityIntegral equationsMathematicsSine and cosine transformsLaplace transformMechanical EngineeringDegrees of freedomMathematical analysisStiffnessFractional calculus010101 applied mathematics020303 mechanical engineering & transportsFourier transformsymbolsmedicine.symptomSettore ICAR/08 - Scienza Delle CostruzioniSafety Researchdescription
In this paper, interval fractional derivatives are presented. We consider uncertainty in both the order and the argument of the fractional operator. The approach proposed takes advantage of the property of Fourier and Laplace transforms with respect to the translation operator, in order to first define integral transform of interval functions. Subsequently, the main interval fractional integrals and derivatives, such as the Riemann–Liouville, Caputo, and Riesz, are defined based on their properties with respect to integral transforms. Moreover, uncertain-but-bounded linear fractional dynamical systems, relevant in modeling fractional viscoelasticity, excited by zero-mean stationary Gaussian forces are considered. Within the interval analysis framework, either exact or approximate bounds of the variance of the stationary response are proposed, in case of interval stiffness or interval fractional damping, respectively.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2017-06-12 |