Positive Solutions for Class of State Dependent Boundary Value Problems with Fractional Order Differential Operators

Abstract

We consider the following state dependent boundary-value problem 0+ ( ) − 0+ ( , ( ( ))) + ( , ( ( ))) = 0, 0 < < 1; (0) = 0, ( (1) Using Banach contraction mapping principle and Leray-Schauder continuation principle, we obtain some sufficient conditions for the existence and uniqueness of the positive solutions for the above fractional order differential equations, which extend some references.