On the existence of mild solutions to some semilinear fractional integro-differential equations
On the existence of mild solutions to some semilinear fractional integro-differential equations
复制标题
DOI：
10.14232/ejqtde.2010.1.58
复制
发表时间：
2010
影响因子：
1.1
通讯作者：
T. Diagana;G. Mophou;G. N’Guérékata
中科院分区：
文献类型：
--
作者：
T. Diagana;G. Mophou;G. N’Guérékata
抽象。研究了一类具非局部条件的分数阶半线性微分方程的温和解的存在性。利用比[12]中更恰当的温和解的定义，我们证明了这样的解的存在性和唯一性，假设线性部分是一个解析半群的无穷小生成元，且该解析半群对t > 0是紧的，非线性部分是关于某个插值空间的范数的Lipschitz连续函数.提供了一个例子。
Abstract. This paper deals with the existence of a mild solution for some fractional semilinear differential equations with non local conditions. Using a more appropriate definition of a mild solution than the one given in [12], we prove the existence and uniqueness of such solutions, assuming that the linear part is the infinitesimal generator of an analytic semigroup that is compact for t > 0 and the nonlinear part is a Lipschitz continuous function with respect to the norm of a certain interpolation space. An example is provided.