一类Conformable分数阶发展方程温和解的存在性  

Existence of Mild Soulutions for a Class of Conformable Fractional Evolution Equations

作　　者：安文艳 杨和 AN Wenyan;YANG He(College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,China)

机构地区：[1]西北师范大学数学与统计学院,兰州730070

出　　处：《吉林大学学报（理学版）》2024年第5期1072-1078,共7页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:12061062)。

摘　　要：用算子半群理论和上下解单调迭代方法讨论Banach空间中具有Volterra型积分算子的一类Conformable分数阶发展方程初值问题{T_(α)u(t)+Au(t)=f(t,u(t),Gu(t)),t∈I,u(0)=x_(0)温和解的存在性,其中:T_(α)表示阶数为0<α<1的Conformable分数阶导数算子;A为稠定闭线性算子,-A:D(A)■E→E生成一致有界的C_(0)-半群T(t)(t≥0);f∈C(I×E×E,E),且I=[0,b];Gu(t)=∫_(0)^(t)K(t,s)u(s)ds是Voletrra型积分算子,其积分核K∈C(Δ,ℝ^(+)),Δ={(t,s)|0≤s≤t≤b},记K_(0)=max_((t,s)∈Δ)K(t,s).在非线性项满足适当的不等式条件下,得到了该方程温和解的存在性.By using operator semigroup theory and upper and lower solution monotone iterative methods,we discuss the existence of mild solutions to initial value problems {T_(α)u(t)+Au(t)=f(t,u(t),Gu(t)),t∈I,u(0)=x_(0) for a class of Conformable fractional evolution equations with Volterra-type integral operators in Banach spaces,where Tαrepresents the Conformable fractional derivative operator with order 0<α<1,A is a coherently closed linear operator,-A:D(A)E→E generate uniformly bounded C_(0)-semigroup T(t)(t≥0),f∈C(I×E×E,E),and I=[0,b],Gu(t)=∫_(0)^(t)K(t,s)u(s)d s is integral operator of Voletrra-type,integral kernel K∈C(Δ,ℝ^(+)),Δ={(t,s)0≤s≤t≤b},recorded as K_(0)=max_((t,s)∈Δ)K(t,s).Under the condition that the nonlinear term satisfies the appropriate inequality,the existence of the mild solution to the equation is obtained.

关 键 词：分数阶发展方程 温和解 上下解 单调迭代方法 

分 类 号：O175.15[理学—数学]