Existence and Uniqueness of Positive Solutions for Caputo Fractional Order Boundary Value Problems

Abstract

A class of two-point boundary value problems whose highest-order term is a Ca puto fractional derivative of order α ∈ (1,2) with a reaction term is considered. It focused on constructing Green’s function for corresponding homogeneous equation by using Laplace transform and Mittag-Leffler function. Under the suitable condi tions, we established the existence of positive solution for Caputo fractional order differential equation BVPs by applying fixed point index theorem. Finally, we established the uniqueness of positive solution for Caputo fractional order differential equation BVPs by applying Banach contraction principle.