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The Existence of Positive Solutions for the Caputo-Fabrizio Fractional Boundary Value Problems at Resonance

This paper deals with a class of nonlinear fractional boundary value problems at resonance with Caputo-Fabrizio fractional derivative. We establish some new necessary conditions for the existence of positive solutions for the fractional boundary value problems at resonance by using the Leggett-Williams norm-type theorem for coincidences due to O' Regan and Zima. Some examples are constructed to support our results.

Keywords:

Fractional Caputo-Fabrizio differential equation, positive solution, resonance necessary condition,

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