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 D_{۰^{+}}^{alpha}x(t)+f(t,x(t))=۰, ۰fixed point theorem in partially ordered sets. An illustrative example is also presented.

Keywords:

Boundary value problem , fixed point theorem , Partially ordered set , Positive solution , nondecreasing solution