隐式分数阶模糊微分方程初值问题解的唯一性

Uniqueness of solutions for initial value problems of implicit fractional order fuzzy differential equations

运用幂压缩映射原理,研究了隐式分数阶模糊微分方程初值问题{u(a)=u_(0)^(C)D_(a+)^(a,p)u(t)=f(t,u(t),^(C)D_(a+)^(a,p)u(t)),解的唯一性,其中0<a<t≤b,α∈(0,1),p>0是给定的实数,(C)D_(a+)^(a,p)是模糊Caputo-Katugampola分数阶广义Hukuhara导数,f:[a,b]×E×E→E是一个模糊函数,E是模糊空间。

By using the principle of power compression mapping,this paper obtains the uniqueness of solution to the initial value problems of implicit fractional fuzzy differential equations{u(a)=u_(0)^(C)D_(a+)^(a,p)u(t)=f(t,u(t),^(C)D_(a+)^(a,p)u(t)),where 0<a<t≤b,α∈(0,1),p>0 is a fixed real number,and(C)D_(a+)^(a,p)is the fuzzy Caputo-Katugampola fractional generalized Hukuhara derivative,f:[a,b]×E×E→E is a fuzzy function.E is the fuzzy space.