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http://hdl.handle.net/10773/41999
Title: | The duality theory of fractional calculus and a new fractional calculus of variations involving left operators only |
Author: | Torres, Delfim F. M. |
Keywords: | Duality Fractional calculus Integration by parts Fractional calculus of variations Euler-Lagrange equations Dissipative systems |
Issue Date: | 2024 |
Publisher: | Springer |
Abstract: | Through duality, it is possible to transform left fractional operators into right fractional operators and vice versa. In contrast to existing literature, we establish integration by parts formulas that exclusively involve either left or right operators. The emergence of these novel fractional integration by parts formulas inspires the introduction of a new calculus of variations, where only one type of fractional derivative (left or right) is present. This applies to both the problem formulation and the corresponding necessary optimality conditions. As a practical application, we present a new Lagrangian that relies solely on left-hand side fractional derivatives. The fractional variational principle derived from this Lagrangian leads us to the equation of motion for a dissipative/damped system. |
Peer review: | yes |
URI: | http://hdl.handle.net/10773/41999 |
DOI: | 10.1007/s00009-024-02652-x |
ISSN: | 1660-5446 |
Publisher Version: | https://doi.org/10.1007/s00009-024-02652-x |
Appears in Collections: | CIDMA - Artigos SCG - Artigos |
Files in This Item:
File | Description | Size | Format | |
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[556]torres-duality.pdf | 389.66 kB | Adobe PDF | View/Open |
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