带有积分边值的Hadamard型积分-微分包含解的存在性

Existence of Solutions for Hadamard-type Fractional Integro-Differential Inclusions with Integral Boundary Value Conditions

利用多值映射的不动点定理,给出了一类带有非局部积分边值Hadamard型分数阶积分微分包含解的存在性定理,得到了解存在性的充分条件,并将已有的单值结果推广到多值情形.

In this paper,based on fixed-point theorem for multi-value maps,we give the existence of solutions for the following Hadamard fractional order integro-differential inclusions with integral boundary value Problems：{Dαx（ t） ∈ F（ t,x（ t））,1 ≤ t ≤ e,1 ≤ α ≤ 2,x（ 1） = x（ 0）,x（ e） =1/Γ（ β） integral from 1 to e （ loge/s）（β-1）x（ s）/sds,β 0,Where Dα is Hadamard type fractional derivative,Kx（ t） = integral from 1 to t k（ t,s,x（ s）） ds is a integral operator,and F：[1,e]× R × R→P（ R） is a multi-valued map. The aim of this paper is to extend known single value result to multi-valued framework.