期刊
APPLIED MATHEMATICS LETTERS
卷 25, 期 2, 页码 142-148出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.aml.2011.08.003
关键词
Calculus of variations; Riesz-Caputo fractional derivative; Isoperimetric problem
资金
- FEDER funds through COMPETE-Operational Programme Factors of Competitiveness (Programa Operacional Factores de Competitividade)
- Center for Research and Development in Mathematics and Applications (University of Aveiro)
- Portuguese Foundation for Science and Technology (FCT-Fundacao para a Ciencia e a Tecnologia) [PEst-C/MAT/UI4106/2011, FCOMP-01-0124-FEDER-022690]
In this paper we investigate optimality conditions for fractional variational problems, with a Lagrangian depending on the Riesz-Caputo derivative. First we prove a generalized Euler-Lagrange equation for the case when the interval of integration of the functional is different from the interval of the fractional derivative. Next we consider integral dynamic constraints on the problem, for several different cases. Finally, we determine optimality conditions for functionals depending not only on the admissible functions, but on time also, and we present a necessary condition for a pair function-time to be an optimal solution to the problem. (C) 2011 Elsevier Ltd. All rights reserved.
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