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.