Positive solutions of conformable fractional differential equations with integral boundary conditions

In this paper, we discuss the existence of positive solutions of the conformable fractional differential equation T alpha X(t)+ f(t,X(t)) = 0, t is an element of [0,1], subject to the boundary conditions X(0) = 0 and X(1) = lambda integral(1)(0) X(t) dt, where the order a belongs to (1,2], T alpha X(t) denotes the conformable fractional derivative of a function X(t) of order alpha, and f : [0,1] x [0, infinity) bar right arrow [0, infinity) is continuous. By use of the fixed point theorem in a cone, some criteria for the existence of at least one positive solution are established. The obtained conditions are generally weaker than those derived by using the classical norm-type expansion and compression theorem. A concrete example is given to illustrate the possible application of the obtained results.