Advances in Differential Equations

On a generalized fractional Du Bois-Reymond lemma and its applications

Rafał Kamocki

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Abstract

In the paper, we derive a fractional version of the Du Bois-Reymond lemma for a generalized Riemann-Liouville derivative (derivative in the Hilfer sense). It is a generalization of well known results of such a type for the Riemann-Liouville and Caputo derivatives. Next, we use this lemma to investigate critical points of a some Lagrange functional (we derive the Euler-Lagrange equation for this functional).

Article information

Source
Adv. Differential Equations, Volume 23, Number 11/12 (2018), 889-908.

Dates
First available in Project Euclid: 25 September 2018

Permanent link to this document
https://projecteuclid.org/euclid.ade/1537840836

Mathematical Reviews number (MathSciNet)
MR3857873

Zentralblatt MATH identifier
06982202

Subjects
Primary: 26A33, 70H03

Citation

Kamocki, Rafał. On a generalized fractional Du Bois-Reymond lemma and its applications. Adv. Differential Equations 23 (2018), no. 11/12, 889--908. https://projecteuclid.org/euclid.ade/1537840836


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