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.
作者
安文艳
杨和
AN Wenyan;YANG He(College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,China)
出处
《吉林大学学报（理学版）》
CAS
北大核心
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)。
关键词
分数阶发展方程
温和解
上下解
单调迭代方法
fractional evolution equation
mild solution
upper and lower solution
monotone iterative method
