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Positivity for integral boundary value problems of fractional differential equations with two nonlinear terms

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Abstract

We investigate a class of integral boundary value problems of fractional differential equations with two nonlinear terms, one is non-monotone and the other contain fractional derivative. Existence of positive solutions is obtained by the method of upper and lower solutions and Schauder fixed point theorem and unique result is presented from Banach contraction mapping principle. Several examples are given to show the applicability of our main results.

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Acknowledgements

The authors sincerely thank the reviewers for their valuable suggestions and useful comments that have led to the present improved version of the original manuscript. This research is supported by Shandong Provincial Natural Science Foundation (ZR2016AM17).

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Jinan, Jinan, 250022, Shandong, People’s Republic of China

    Mengrui Xu & Shurong Sun

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  1. Mengrui Xu
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  2. Shurong Sun
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Correspondence to Shurong Sun.

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Xu, M., Sun, S. Positivity for integral boundary value problems of fractional differential equations with two nonlinear terms. J. Appl. Math. Comput. 59, 271–283 (2019). https://doi.org/10.1007/s12190-018-1179-7

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  • DOI: https://doi.org/10.1007/s12190-018-1179-7

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