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AIMS Mathematics

2020, Volume 5, Issue 6: 7359-7371. doi: 10.3934/math.2020471
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Properties of positive solutions for a fractional boundary value problem involving fractional derivative with respect to another function

  • College of Science, Tianjin University of Technology, Tianjin 300384, China
  • Received: 04 August 2020 Accepted: 16 September 2020 Published: 18 September 2020

  • MSC : 34A08, 34A12

  • In this article, we develop the existence and uniqueness of positive solutions to a class of fractional boundary value problems involving fractional order derivative with respect to another function for any given parameter. The analysis is based upon the fixed point theorems of concave operators in partial ordering Banach spaces. For the sake of discussing the existence of solutions for the problem, we first construct Green function and study its properties. Furthermore, some properties of positive solutions to the boundary value problem are proved under the different parameters. Examples illustrating the results are also presented.

    Citation: Yitao Yang, Dehong Ji. Properties of positive solutions for a fractional boundary value problem involving fractional derivative with respect to another function[J]. AIMS Mathematics, 2020, 5(6): 7359-7371. doi: 10.3934/math.2020471

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  • In this article, we develop the existence and uniqueness of positive solutions to a class of fractional boundary value problems involving fractional order derivative with respect to another function for any given parameter. The analysis is based upon the fixed point theorems of concave operators in partial ordering Banach spaces. For the sake of discussing the existence of solutions for the problem, we first construct Green function and study its properties. Furthermore, some properties of positive solutions to the boundary value problem are proved under the different parameters. Examples illustrating the results are also presented.


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