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In this article we present a new fixed point theorem for a class of generalized concave operators and we establish some properties of positive solutions for the operator equation $Ax=\lambda x$. Based on them, the existence and uniqueness of positive solutions for a class of fractional differential equations with integral boundary conditions is proved. Moreover, we present some properties of positive solutions to the boundary value problem dependent on the parameter.

advances in difference equations

Properties of positive solutions for the operator equation A x = λ x $Ax=\lambda x$ and applications to fractional differential equations with integral boundary conditions