What is it about?
In this article, we prove the existence and uniqueness of solution for some higher-order fractional differential equations with conjugate type integral conditions. The interesting point lies in that the Lipschitz constant is closely associated with the first eigenvalues corresponding to the relevant linear operator. The discussion is based on the Banach contraction map principle and the theory of u0-positive linear operator.
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Why is it important?
Derivatives of two different arbitrary orders and parameter \lambda in the BCs makes the problems studied here perform more general form. The Lipschitz constant imposed on the nonlinearity is associated with the first eigenvalues corresponding to the relevant linear operator which is essential to a linear operator. The properties of the Green function are focused on which is of some great technique.
Perspectives
I hope this article makes people concentrate on investigating the existence of unique or multiplicity of positive or sign-changing solutions under more general nonlocal BVPs from several different viewpoints which is one of important direction in the field of fractional differential equations. More than anything else, and if nothing else, I hope you find this article thought-provoking.
Xingqiu Zhang
Jining Medical University
Read the Original
This page is a summary of: Uniqueness of solution for higher-order fractional differential equations with conjugate type integral conditions, Fractional Calculus and Applied Analysis, December 2017, De Gruyter,
DOI: 10.1515/fca-2017-0077.
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