分数变分微积分研究综述

Basic Theory Pub Date : 2018-06-13 DOI:10.1515/9783110571622-014

R. Almeida, Delfim F. M. Torres

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引用次数: 6

摘要

综述了分数变分学的主要成果和技术。我们考虑了包含卡普托导数的变分问题，并用间接和直接方法研究了它们。特别地，我们为基本问题、高阶问题和等周期问题提供了必要的Euler-Lagrange型最优性条件，并基于截断的Caputo导数的Grunwald—Letnikov近似计算了近似解。

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A survey on fractional variational calculus

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 Grunwald--Letnikov approximations of Caputo derivatives.

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Basic Theory

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