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Analyzing the dynamics of deterministic systems from a hypergraph theoretical point of view

Luis M. TorresAnnegret K. Wagler — 2013

RAIRO - Operations Research - Recherche Opérationnelle

To model the dynamics of discrete deterministic systems, we extend the Petri nets framework by a priority relation between conflicting transitions, which is encoded by orienting the edges of a transition conflict graph. The aim of this paper is to gain some insight into the structure of this conflict graph and to characterize a class of suitable orientations by an analysis in the context of hypergraph theory.

Calculus of Variations with Classical and Fractional Derivatives

Odzijewicz, TatianaTorres, Delfim F. M. — 2012

Mathematica Balkanica New Series

MSC 2010: 49K05, 26A33 We give a proper fractional extension of the classical calculus of variations. Necessary optimality conditions of Euler-Lagrange type for variational problems containing both classical and fractional derivatives are proved. The fundamental problem of the calculus of variations with mixed integer and fractional order derivatives as well as isoperimetric problems are considered.

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