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Existence of Solutions of Nonlinear and Non-local Fractional Boundary Value Problems

  • Alberto Cabada
  • Suzana Aleksić
  • Tatjana V. Tomović
  • Sladjana DimitrijevićEmail author
Article
  • 96 Downloads

Abstract

In this paper, we establish new results for non-local boundary value problems. In particular, we study a fractional differential equation where the associated integral equation has a kernel that is not bounded above and changes its sign, so that, the positive sign of the possible solutions is generally not ensured. We provide some examples which support the theory and illustrate the applicability of the obtained results.

Keywords

Fractional differential equation non-local boundary value problem positive solution Caputo’s fractional derivative Green’s function 

Mathematics Subject Classification

34A08 34B10 34B15 

Notes

Acknowledgements

First author partially is supported by Xunta de Galicia (Spain), project EM2014/032 and AIE Spain and FEDER, Grant MTM2016-75140-P.

Second, third and fourth authors are supported by Serbian Ministry of Science and Technology (Grants 174024 and 174015).

The authors are very grateful to the reviewer of the work. His/her suggestions have been fundamental for the improvement of this article.

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Authors and Affiliations

  1. 1.Departamento de Estatística, Análise Matemática e Optimización Instituto de Matemáticas, Facultade de MatemáticasUniversidade de Santiago de CompostelaSantiago de CompostelaSpain
  2. 2.Department of Mathematics and InformaticsFaculty of Science, University of KragujevacKragujevacSerbia

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