Fractional Derivatives in Interval Analysis

Giulio Cottone, Giulio Cottone

    Research output: Contribution to journalArticlepeer-review

    Abstract

    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.
    Original languageEnglish
    Pages (from-to)030907-
    Number of pages6
    JournalASCE-ASME JOURNAL OF RISK AND UNCERTAINTY IN ENGINEERING SYSTEMS. PART B. MECHANICAL ENGINEERING
    Volume3
    Publication statusPublished - 2017

    All Science Journal Classification (ASJC) codes

    • Safety, Risk, Reliability and Quality
    • Safety Research
    • Mechanical Engineering

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