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

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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.

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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. Departamento de Estatística, Análise Matemática e Optimización Instituto de Matemáticas, Facultade de Matemáticas, Universidade de Santiago de Compostela, Santiago de Compostela, Galicia, Spain

    Alberto Cabada

  2. Department of Mathematics and Informatics, Faculty of Science, University of Kragujevac, Kragujevac, Serbia

    Suzana Aleksić, Tatjana V. Tomović & Sladjana Dimitrijević

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  1. Alberto Cabada
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  2. Suzana Aleksić
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  3. Tatjana V. Tomović
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  4. Sladjana Dimitrijević
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Correspondence to Sladjana Dimitrijević.

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Cabada, A., Aleksić, S., Tomović, T.V. et al. Existence of Solutions of Nonlinear and Non-local Fractional Boundary Value Problems. Mediterr. J. Math. 16, 119 (2019). https://doi.org/10.1007/s00009-019-1388-9

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  • DOI: https://doi.org/10.1007/s00009-019-1388-9

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