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Distributed-order calculus: An operator-theoretic interpretation

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Abstract

Within the Bochner-Phillips functional calculus and Hirsch functional calculus, we describe the operators of distributed-order differentiation and integration as functions of the classical operators of differentiation and integration, respectively.

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Author information

Correspondence to A. N. Kochubei.

Additional information

Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 4, pp. 478–486, April, 2008.

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Kochubei, A.N. Distributed-order calculus: An operator-theoretic interpretation. Ukr Math J 60, 551 (2008). https://doi.org/10.1007/s11253-008-0076-x

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Keywords

  • Functional Calculus
  • Fractional Integration Operator
  • Bernstein Function
  • Differential Operator Equation
  • Abel Equation