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Received March 21, 2019; Accepted January 4, 2020; Published January 19, 2020
Abstract. In this paper, we consider a boundary value problem of Hadamard fractional differential equations on an infinite interval
where is the Hadamard fractional derivative of order , , denotes the Hadamard fractional integral, is a parameter, are constants and The existence and uniqueness of positive solutions is given for each fixed The relations between the positive solution and the parameter are presented. The results obtained in this paper show that the unique positive solution has good properties: continuity, monotonicity, iteration and approximation. The method of this paper is based upon different fixed point theorems and properties for two types of operators: monotone operators and mixed monotone operators. Finally, two examples are also provided.
How to Cite this Article:
Ruixiong Fan, Weixuan Wang, Chengbo Zhai, Positive solutions for Hadamard fractional boundary value problems on an infinite interval, Journal of Nonlinear Functional Analysis, Vol. 2020 (2020), Article ID 2, pp. 1-14.