带有非局部积分边值的Hadamard型分数阶微分包含解的终结点型存在性定理

Endpoint theorem on existence of solutions for Hadamard-type fractional differential inclusions with nonlocal integral boundary value conditions

利用多值映射的不动点定理,给出了以下带有非局部积分边值Hadamard型分数阶微分包含解的终结点型存在性定理:{Dαx(t)∈F(t,x(t)),1<t<e,1<α≤2,x(1)=x(0),A/Γ(γ)∫η1(logη/s)γ-1x(s)/s ds+Bx(e)=c,γ>0,1<η<e},其中D~α表示Hadamard型分数阶导数,F:[1,e]×R→P(R)是多值映射,A,B,c是常数。所得结果将已有的单值结果推广到多值情形。

Based on fixed-point theorem for multi-value maps, the endpoint theorem on the existence of solutions for the following Hadamard fractional order differential inclusions with nonlocal integral boundary value problems is given：{Dαx（t）∈F（t,x（t））,1〈t〈e,1〈α≤2,x（1）=x（0）,A/Г（γ）∫η1（logη/s）γ-1x（s）/sds＋Bx（e）=c,γ〉0,1〈η〈ewhere Dα is Hadamard type fractional derivative, F： [1, e]×R→2（R） is a multi-valued map, A, B, c are constants. The aim of this paper is to extend known single value result to multi-valued framework.