Uniqueness of solution for higher-order fractional differential equations with conjugate type integral conditions

In this article, we prove the existence and uniqueness of solution for some higher-order fractional differential equations with conjugate type integral conditions. The interesting point lies in that the Lipschitz constant is closely associated with the first eigenvalues corresponding to the relevant linear operator. The discussion is based on the Banach contraction map principle and the theory of u 0 -positive linear operator.