Cauchy-Lipschitz theory for fractional multi-order dynamics - State-transition matrices, Duhamel formulas and duality theoremsReport as inadecuate




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1 XLIM-MATHIS - Mathématiques & Sécurité de l-information XLIM - XLIM : MATHIS

Abstract : The aim of the present paper is to contribute to the development of the study of Cauchy problems involving Riemann-Liouville and Caputo fractional derivatives.
Firstly existence-uniqueness results for solutions of non-linear Cauchy problems with vector fractional multi-order are addressed.
A qualitative result about the behavior of local but non-global solutions is also provided.
Finally the major aim of this paper is to introduce notions of fractional state-transition matrices and to derive fractional versions of the classical Duhamel formula.
We also prove duality theorems relying left state-transition matrices with right state-transition matrices.






Author: Loïc Bourdin -

Source: https://hal.archives-ouvertes.fr/



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