Please use this identifier to cite or link to this item:
http://hdl.handle.net/10773/11889
Title: | Discrete direct methods in the fractional calculus of variations |
Author: | Pooseh, S. Almeida, R. Torres, D.F.M. |
Keywords: | Direct methods Fractional calculus Fractional calculus of variations Mesh points Minimization problems Riemann-Liouville fractional derivatives Static optimization Variational problems Mathematical models Algorithms |
Issue Date: | Sep-2013 |
Publisher: | Elsevier |
Abstract: | Finite differences, as a subclass of direct methods in the calculus of variations, consist in discretizing the objective functional using appropriate approximations for derivatives that appear in the problem. This article generalizes the same idea for fractional variational problems. We consider a minimization problem with a Lagrangian that depends on the left Riemann-Liouville fractional derivative. Using the Grünwald-Letnikov definition, we approximate the objective functional in an equispaced grid as a multi-variable function of the values of the unknown function on mesh points. The problem is then transformed to an ordinary static optimization problem. The solution to the latter problem gives an approximation to the original fractional problem on mesh points. |
Peer review: | yes |
URI: | http://hdl.handle.net/10773/11889 |
DOI: | 10.1016/j.camwa.2013.01.045 |
ISSN: | 0898-1221 |
Appears in Collections: | CIDMA - Artigos DMat - Artigos |
Files in This Item:
File | Description | Size | Format | |
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[258]PoosehAlmeidaTorresDMethodIFA.pdf | 407.16 kB | Adobe PDF |
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