A fractional fundamental lemma and a fractional integration by parts formula -- Applications to critical points of Bolza functionals and to linear boundary value problems
A fractional fundamental lemma and a fractional integration by parts formula -- Applications to critical points of Bolza functionals and to linear boundary value problems
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DOI：
10.57262/ade/1423055200
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发表时间：
2014-02
影响因子：
1.4
通讯作者：
L. Bourdin;D. Idczak
中科院分区：
文献类型：
--
作者：
L. Bourdin;D. Idczak
在本文的第一部分，我们证明了分式基本(Du Bois-Reymond)引理和分部积分公式的分式变式。第二个结果的证明也是基于本文推导出的具有Riemann-Liouville分数导数的函数的积分表示。在本文的第二部分，我们利用前面的结果给出了分数次Bolza泛函的Euler-Lagrange型(带边界条件)的最优性必要条件，并证明了线性分数次边值问题解的存在性结果。在最后一种情况下，我们使用希尔伯特结构和Stampacchia定理。
In the first part of the paper, we prove a fractional fundamental (du Bois-Reymond) lemma and a fractional variant of the integration by parts formula. The proof of the second result is based on an integral representation of functions possessing Riemann-Liouville fractional derivatives, derived in this paper too. In the second part of the paper, we use the previous results to give necessary optimality conditions of Euler-Lagrange type (with boundary conditions) for fractional Bolza functionals and to prove an existence result for solutions of linear fractional boundary value problems. In the last case we use a Hilbert structure and the Stampacchia theorem.