Existence and uniqueness of positive and nondecreasing solution for nonlocal fractional boundary value problem

In this article, we verify existence and uniqueness of positive and nondecreasing solution for nonlinear boundary value problem of fractional differential equation in the form Dalpha0+x(t)+f(t,x(t))=0,0 t 1,2 alpha 3,x(0)=x′(0)=0,x′(1)=betax(xi), where Dalpha0+ denotes the standard Riemann-Liouville fractional derivative,0 xi 1 and 0 βξα−1 α−1 Our analysis relies a fixed point theorem in partially ordered sets. An illustrative example is also presented.