分数阶模糊微分方程周期边值问题解的存在唯一性

Existence and Uniqueness of Solutions to Periodic Boundary Value Problems for Fractional Fuzzy Differential Equations

运用偏序集上弱压缩映射的不动点定理,研究分数阶模糊微分方程周期边值问题{CgHD^(q)_(*)u(t)=f(t,u(t)),t∈(0,T),u(0)=λu(T)解的存在唯一性,其中,CgHD^(q)_(*)是Caputo分数阶广义Hukuhara导数,q∈(0,1],λ∈[0,1)∪(1,+∞),f:[0,T]×E→E是连续的模糊数值函数.

By using the fixed point theorem of weakly contracted mappings on partially ordered sets,we obtain the existence and uniqueness of solutions to periodic boundary value problems for fractional fuzzy differential equations {CgHD^(q)_(*)u(t)=f(t,u(t)),t∈(0,T)u(0)=λu(T),where CgHD^(q)_(*) is the Caputo fractional generalized Hukuhara derivative,q∈(0,1],λ∈[0,1)∪(1,+∞),f:[0,T]×E→E is a continuous fuzzy numerical function.