Positive solutions for a class of integral boundary value condition of fractional differential equations with a parameter

Volume 10, Issue 5, pp 2710--2718 http://dx.doi.org/10.22436/jnsa.010.05.37

Publication Date: May 25, 2017 Submission Date: September 28, 2016

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Authors

Chen Yang - Basic Course Department, Business College of Shanxi University, Taiyuan 030031, Shanxi, P. R. China.

Abstract

In this work, we study a class of integral boundary value condition of fractional differential equations with a parameter. The existence and uniqueness of positive solutions to the boundary value problem is established. Further, we present some properties of positive solutions to the boundary value problem dependent on the parameter. The method employed is a fixed point theorem of concave operators in partial ordering Banach spaces. As applications, two examples are given to illustrate our main results.

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Keywords

• Fractional order derivative
• positive solution
• parameter
• fixed point theorem of concave operator
• integral boundary value condition.

MSC

•  26A33
•  34B18
•  34B27

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