Distributed Order Calculus: an Operator-Theoretic Interpretation
Anatoly N. Kochubei
TL;DR
This paper provides an operator-theoretic interpretation of distributed order calculus by representing differentiation and integration operators as functions within established functional calculi frameworks.
Contribution
It introduces a novel interpretation of distributed order operators as functions of classical operators using Bochner-Phillips and Hirsch calculi.
Findings
Distributed order differentiation and integration are expressed as functions of classical operators.
The approach unifies distributed order calculus with operator theory frameworks.
Provides a new perspective for analyzing distributed order operators.
Abstract
Within the functional calculi of Bochner-Phillips and Hirsch, we describe the operators of distributed order differentiation and integration as functions of the classical differentiation and integration operators respectively.
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Taxonomy
TopicsStochastic processes and financial applications · advanced mathematical theories · Matrix Theory and Algorithms