非线性Caputo-Hadamard型分数阶微分包含正解的存在性

Existence of positive solutions for nonlinear caputo-hadamard fractional differential inclusions with integral boundary value conditions

通过多值映射的不动点定理,证明了如下一类带有积分边值条件的Caputo-Hadamard分数阶微分包含问题多个正解的存在性:{^(CH)D^(α)x(t)∈F(t,x(t)),1<t≤e x(1)=λ∫_(1)^(e)x(s)ds+d,其中^(CH)Dα代表Caputo-Hadamard分数阶导数,1/2<α≤1,0≤λ<1/e-1,d>0,F:[1,e]×R→p(R)的多值映射,p(R)表示R上所有非空子集。

By the fixed point theorem of multi-valued mappings,we obtain the existence theorem of at least two positive solutions for the following problem of Caputo-Hadamard fractional differential inclusion with integral boundary value condition:{^(CH)D^(α)x(t)∈F(t,x(t)),1<t≤e x(1)=λ∫_(1)^(e)x(s)ds+d,其中^(CH)D^(α),where ^(CH)D^(α) denotes the Caputo-Hadamard fractional derivative,1/2<α≤1,0≤λ<1/e-1,d>0,F:[1,e]×R→p(R)is a multivalued map,p(R)is the family of all subsets of R.