Translator Disclaimer
July/August 2018 Cauchy-Lipschitz theory for fractional multi-order dynamics: State-transition matrices, Duhamel formulas and duality theorems
Loïc Bourdin
Differential Integral Equations 31(7/8): 559-594 (July/August 2018).

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. First, 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.

Citation

Download Citation

Loïc Bourdin. "Cauchy-Lipschitz theory for fractional multi-order dynamics: State-transition matrices, Duhamel formulas and duality theorems." Differential Integral Equations 31 (7/8) 559 - 594, July/August 2018.

Information

Published: July/August 2018
First available in Project Euclid: 11 May 2018

zbMATH: 06890405
MathSciNet: MR3801825

Subjects:
Primary: 26A33, 34A08, 34A12, 34A30, 34A34

Rights: Copyright © 2018 Khayyam Publishing, Inc.

JOURNAL ARTICLE
36 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.31 • No. 7/8 • July/August 2018
Back to Top