MULTIPLE POSITIVE SOLUTIONS FOR A SYSTEM OFFRACTIONAL HIGHER-ORDER INFINITE-POINT BOUNDARY VALUE PROBLEMS

Özet

In this article, we establish some results on the existence of multiple positivesolutions for a system of nonlinear fractional order infinite-point boundary value prob-lems. The main tool is a fixed point theorem of the cone expansion and compression offunctional 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 byapplying the five functional fixed point theorem. And then, we establish the existenceof at least 2k−1 positive solutions to the fractional order boundary value problems forany arbitrary positive integer k.