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Generalized Hukuhara Differentiability of Interval-valued Functions and Interval Differential Equations

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Author Info

  • Luciano Stefanini

    ()
    (Dipartimento di Economia e Metodi Quantitativi, Università di Urbino (Italy))

  • Barnabas Bede

    ()
    (Department of Mathematics, University of Texas-Pan American, Edimburg, Texas (USA))

Abstract

In the present paper we introduce and study a generalization of the Hukuhara differ- ence and also generalizations of the Hukuhara differentiability to the case of interval valued functions. We consider several possible definitions for the derivative of an interval valued function and we study connections between them and their proper- ties. Using these concepts we study interval differential equations. Local existence and uniqueness of two solutions is obtained together with characterizations of the solutions of an interval differential equation by ODE systems and by differential algebraic equations. We also show some connection with differential inclusions. The thoretical results are turned into practical algorithms to solve interval differential equations.

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File URL: http://www.econ.uniurb.it/RePEc/urb/wpaper/WP_08_03.pdf
File Function: First version, 2008
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Bibliographic Info

Paper provided by University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini in its series Working Papers with number 0803.

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Length: 39 pages
Date of creation: 2008
Date of revision: 2008
Handle: RePEc:urb:wpaper:08_03

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Web page: http://www.econ.uniurb.it/
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Related research

Keywords: Interval Arithmetic; Interval Differentiability; Hukuhara Difference; Hukuhara Derivative; Interval Differential Equations.;

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References

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  1. Luciano Stefanini, 2008. "A generalization of Hukuhara difference for interval and fuzzy arithmetic," Working Papers 0801, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2008.
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Cited by:
  1. Luciano Stefanini & Barnabás Bede, 2012. "Some notes on generalized Hukuhara differentiability of interval-valued functions and interval differential equations," Working Papers 1208, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2012.
  2. Barnabás Bede & Luciano Stefanini, 2012. "Generalized Differentiability of Fuzzy-valued Functions," Working Papers 1209, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2012.
  3. Luciano Stefanini & Barnabás Bede, 2012. "Generalized Fuzzy Differentiability with LU-parametric Representation," Working Papers 1210, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2012.

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