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

BAI Ding-yong

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Journal of Guangzhou University(Natural Science Edition) ›› 2014, Vol. 13 ›› Issue (4) : 1-10.

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

  • BAI Ding-yong
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Abstract

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.

Key words

fractional variational problems / Riemann-Liouville fractional derivative / Du Bois-Reymond Lemma / α-order weak local minimum / Euler equation / global minimum

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BAI Ding-yong. Du Bois-Reymond‘s type lemmas of fractional derivatives and its applications in fractional variational problems. Journal of Guangzhou University(Natural Science Edition). 2014, 13(4): 1-10

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