Existence and multiple positive solutions to systems of differential equations of fractional order

We show under some conditions the existence and multiplicity of positive solutions for a system of differential equations of fractional order, subject to two-point boundary conditions by applying the fixed point index theory in cones.Publisher's Versio

Existence and nonexistence of positive solutions for a n-th order three-point boundary value problem

The purpose of this paper is to establish some results on the existence and nonexistence of positive solutions for a type of nonlinear n-th order three-point boundary value problems. The main tool is a fixed point theorem of the cone expansion and compression of functional type due to Avery, Anderson, and O’Regan. Some examples are presented to illustrate the availability of the main results.Publisher's Versio

Multiple positive solutions for a system of fractional higher-order infinite-point boundary value problems

In this article, we establish some results on the existence of multiple positive solutions for a system of nonlinear fractional order infinite-point boundary value problems. The main tool is a fixed point theorem of the cone expansion and compression of functional type due to Avery, Anderson and O’Regan for at least one positive solution. We also prove that the boundary value problems has at least three positive solutions by applying the five functional fixed point theorem. And then, we establish the existence of at least 2k − 1 positive solutions to the fractional order boundary value problems for any arbitrary positive integer k.Publisher's Versio