【作者】 罗堃；

【导师】 张传义；

【作者基本信息】 哈尔滨工业大学 ， 基础数学， 2010， 硕士

【摘要】 本文主要包括三部分内容:第一部分介绍概周期型函数空间的逐步扩张及相关性质;第二部分介绍了整数阶微分方程的概周期型解的相关理论;最后一部分是关于分数阶微分方程的概周期型解的相关理论。概周期函数理论是由Danish的数学家H.Bohr于1925—1926首先提出来的,后来由S.Bochner,H.Weyl, A.Besicovitch, V.V.Stepanov等人发展了他的理论。分数阶微积分运算包括分数阶微分运算和分数阶积分运算,它的含义就是将普通意义下的微积分运算的运算阶次从整数阶推广到分数和复数的情况。在相关的文章中,作者Daniela Araya等引入了? -预解族的概念,证明了Riemann-Liouville分数阶微分方程在适当条件下概自守适度解的存在性;之后,作者Hui-Sheng等对该文中的条件进行放宽,得到了相似的结论。在本文中,我们利用Banach不动点定理得到了分数阶微分方程在适当条件下伪概周期解的存在唯一性,并在某种程度上推广了前人的结果。更多还原

【Abstract】 This paper consists of three parts: the first part introduces the space of almost periodic type functions and the related nature of the gradual expansion; the second part describes the interger-order differential equations of the almost periodic solutions of relevant theories; the last part takes on the existence and uniqueness of almost periodic type solutions of abstract fractional differential equations.Theory of almost periodic function was first proposed by Danish mathematician H. Bohr in 1925-1926, and later was developed by S. Bochner, H. Weyl, A. Besicovitch, and V.V.Stepanov. Fractional calculus includes fractional derivatives and fractional integrals. It means to generalize the differentiation and integration into fractional and complex order. In a related article, the authors Daniela Araya introduced the concept of ? -resolvent families to prove the existence of almost automorphic mild solutions to the following fractional differential equation in the sense of Riemann-Liouville. Later, the author Hui-Sheng relaxed the conditions in literature and obtained the same results.In this paper, we utilize Banach fix-point theorem to get pseudo almost periodic mild solutions and pseudo almost automorphic mild solutions which extends the results in the paper introduced before to a certain extent under appropriate assumptions.更多还原