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## A Filippov's Theorem on Existence of Solutions for Fraction Differential Inclusions with Multi-Point Boundary Value Conditions

YANG Dan-dan;School of Mathematical Science,Huaiyin Normal University;
In many research fields,some practical problems could be established to fractional differential equation models or fractional differential inclusion models for study,which have been got much attention by mathematicians in recent years. In 2016,in paper[8] the authors investigated the existence of solutions for a class of fractional differential equations. In this paper,based on fixed-point theorem for multi-value maps,we are concerned with the following fractional order differential inclusions with multi-point boundary value problems:D~αy( t) ∈ F( t,y( t)),t ∈ [0,T],T 0,y( T) = y~*+ h( y),D~Py( T) =m∑i = 1D~py( ηi),where 1 α≤2,0 p 1,D~α,D~p denote Caputo derivatives,x~*∈ R,0 η_i T,i = 1,2,3,...,m. h:[0,T] × R→ R is a continuous,F:[0,T]× R → P(R) in[0,T]is a multi-valued map. The Filippove theorem on the existence solutions for the problem is given. The aim of this paper is to extend known single value result[8] to multi-value framework.
【Fund】： 国家自然科学基金项目(11426141);; 江苏省自然科学基金项目(BK20151288)
【CateGory Index】： O175.8
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