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Title: Optimality conditions for fractional variational problems with free terminal time
Author: Almeida, Ricardo
Keywords: Fractional calculus
Euler–Lagrange equation
Legendre condition
Isoperimetric problem
Issue Date: 2018
Publisher: American Institute of Mathematical Sciences
Abstract: This paper provides necessary and sufficient conditions of optimality for variational problems that deal with a fractional derivative with respect to another function. Fractional Euler–Lagrange equations are established for the fundamental problem and when in presence of an integral constraint. A Legendre condition, which is a second-order necessary condition, is also obtained. Other cases, such as the infinite horizon problem, the problem with delays in the Lagrangian, and the problem with high-order derivatives, are considered. Finally, a necessary condition for the optimal fractional order to satisfy is proved.
Peer review: yes
DOI: 10.3934/dcdss.2018001
ISSN: 1937-1632
Appears in Collections:CIDMA - Artigos
SCG - Artigos

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