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http://hdl.handle.net/10773/15039
Title: | Duality for the left and right fractional derivatives |
Author: | Caputo, M. Cristina Torres, Delfim F. M. |
Keywords: | Fractional derivatives and integrals Duality theory Fractional integration by parts Calculus of variations Existence of solutions |
Issue Date: | Feb-2015 |
Publisher: | Elsevier |
Abstract: | We prove duality between the left and right fractional derivatives, independently on the type of fractional operator. Main result asserts that the right derivative of a function is the dual of the left derivative of the dual function or, equivalently, the left derivative of a function is the dual of the right derivative of the dual function. Such duality between left and right fractional operators is useful to obtain results for the left operators from analogous results on the right operators and vice versa. We illustrate the usefulness of our duality theory by proving a fractional integration by parts formula for the right Caputo derivative and by proving a Tonelli-type theorem that ensures the existence of minimizer for fractional variational problems with right fractional operators. (C) 2014 Elsevier B.V. All rights reserved. |
Peer review: | yes |
URI: | http://hdl.handle.net/10773/15039 |
DOI: | 10.1016/j.sigpro.2014.09.026 |
ISSN: | 0165-1684 |
Appears in Collections: | CIDMA - Artigos |
Files in This Item:
File | Description | Size | Format | |
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1409.5319v1.pdf | 190.32 kB | Adobe PDF | View/Open |
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