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- 2018
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
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Abstract:
摘要： 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 e, 1<α≤2, x(1)=x(0), A/( Γ(γ))∫ η 1( logη/s) γ-1(x(s))/s ds+Bx( e)=c, γ>0, 1<η< e, 其中 Dα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。
Abstract: 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 e, 1<α≤2, x(1)=x(0), A/( Γ(γ))∫ η 1( logη/s) γ-1(x(s))/s ds+Bx( e)=c, γ>0, 1<η< e, where Dα is Hadamard type fractional derivative, F:［1, e］×R→P(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
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