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

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URI: https://hdl.handle.net/10347/45153
ISSN: 1660-5446
E-ISSN: 1660-5454
DOI: 10.1007/s00009-019-1388-9

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2019-08-17

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

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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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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).

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Centro de Investigación e Tecnoloxía Matemática de Galicia (CITMAga)
Estatística, Análise Matemática e Optimización