分数阶导数的Du Bois-Reymond引理及其在分数变分问题中的应用（英文）

Du Bois-Reymond's type lemmas of fractional derivatives and its applications in fractional variational problems

考虑Riemann-Liouville分数导数意义下的分数变分问题.首先,对于这类分数变分计算,证明了与古典Du Bois-Reymond引理相对应的结果.然后,应用该结果建立了分数变分泛函的Euler必要条件.最后,讨论了全局极值问题,得到了一些全局极值存在的充分必要条件.

The paper concerns with fractional variational problems in terms of the Riemann-Liouville fractional derivative.First, for such kinds of fractional variational calculus , we prove a counterpart of the Du Bois-Reymond lemma in the classical calculus of variations .Then, this result is applied to establish the Euler necessary conditions on fractional variational functionals .Finally, we discuss the global minimum problems and obtain some sufficient and necessary conditions on the existence of global minimum .