Positive solutions of two-point boundary value problems of nonlinear fractional differential equation at resonance

Abstract

This paper is concerned with a kind of nonlinear fractional differential boundary value problem at resonance with Caputo's fractional derivative. Our main approach is the recent Leggett-Williams norm-type theorem for coincidences due to O'Regan and Zima. The most interesting point is the acquisition of positive solutions for fractional differential boundary value problem at resonance. Moreover, an example is constructed to show that our result here is valid.

Keywords

• fractional differential equation
• resonance
• cone
• positive solution