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arXiv · 1806.05092

A survey on fractional variational calculus

Ricardo Almeida·Delfim F. M. Torres
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Abstract

Main results and techniques of the fractional calculus of variations are surveyed. We consider variational problems containing Caputo derivatives and study them using both indirect and direct methods. In particular, we provide necessary optimality conditions of Euler-Lagrange type for the fundamental, higher-order, and isoperimetric problems, and compute approximated solutions based on truncated Grünwald--Letnikov approximations of Caputo derivatives.

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Ricardo Almeida, Delfim F. M. Torres. 2018-06-13. A survey on fractional variational calculus. https://doi.org/10.1515/9783110571622-014

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