Properties of positive solutions to a class of four-point boundary value problem of Caputo fractional differential equations with a parameter

• We study a four-point boundary value problem of Caputo fractional differential equations.
• The existence and uniqueness of positive solutions are established.
• The methods are fixed point theorems of concave operators in ordered Banach spaces.
• We present some pleasant properties of the positive solutions dependent on the parameter.
• Two examples are given to illustrate our main results.

In this paper, by using fixed point theorems of concave operators in partial ordering Banach spaces, we establish the existence and uniqueness of positive solutions to a class of four-point boundary value problem of Caputo fractional differential equations for any given parameter. Moreover, we present some pleasant properties of positive solutions to the boundary value problem dependent on the parameter. In the end, two examples are given to illustrate our main results.