The Nehari manifold for a boundary value problem involving Riemann–Liouville fractional derivative

Journal article

Authors/Editors

POOM KUMAM

Strategic Research Themes

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Publication Details

Author list: Saoudi K., Agarwal P., Kumam P., Ghanmi A., Thounthong P.

Publisher: SpringerOpen

Publication year: 2018

Journal: Advances in Difference Equations (1687-1839)

Volume number: 2018

Issue number: 1

ISSN: 1687-1839

eISSN: 1687-1847

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-85051090333&doi=10.1186%2fs13662-018-1722-8&partnerID=40&md5=407b4481dcf8d727c2ec2b6673dc9630

Languages: English-Great Britain (EN-GB)

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Abstract

We aim to investigate the following nonlinear boundary value problems of fractional differential equations: (Pλ){−tD1α(|0Dtα(u(t))|p−20Dtαu(t))=f(t,u(t))+λg(t)|u(t)|q−2u(t)(t∈(0,1)),u(0)=u(1)=0, where λ is a positive parameter, 2 < r< p< q, 12<α<1, g∈ C([0 , 1]) , and f∈ C([0 , 1] × R, R). Under appropriate assumptions on the function f, we employ the method of Nehari manifold combined with the fibering maps in order to show the existence of solutions to the boundary value problem for the nonlinear fractional differential equations with Riemann–Liouville fractional derivative. We also present an example as an application. © 2018, The Author(s).

Keywords

Riemann–Liouville and Caputo fractional derivative