Banach空间中预解算子控制的一类分数阶微分方程  

On a Fractional Differential Equations via Resolvent Operators in Banach Spaces

作　　者：陈丽珍[1] 李刚[2] 

机构地区：[1]山西财经大学应用数学学院,山西太原030006 [2]扬州大学数学科学学院,江苏扬州225002

出　　处：《山西大学学报（自然科学版）》2015年第3期447-452,共6页Journal of Shanxi University(Natural Science Edition)

基　　金：国家自然科学基金(11271316);山西财经大学青年科研基金(Z06045)

摘　　要：研究了一类带有非局部条件的分数阶微分方程。许多文献在研究同样问题或类似问题时,对应的算子生成一个C0半群,而预解算子没有半群很好的性质,包括算子范数的一致连续性。文章利用凸幂凝聚算子的不动点定理结合解析预解算子理论,讨论了Banach空间中预解算子控制的一类分数阶微分方程温和解的存在性。证明过程中,既没有对Banach空间附加任何条件,也没有假设预解算子的紧性,因此推广和改进了一些已知的结果。最后,给出了定理的若干应用。We discuss the problem of nonlocal fractional differential equations.The problem has been studied by many authors.In all those papers,there are imposed conditions requiring the operator generates a semigroup,but there is no property of semigroups for resolvent,including the continuity of resolvent in the uniform operator topology.In this paper,we establish the existence results for nonlocal fractional differential equations governed by a linear closed operator in Banach spaces by means of analytic resolvent method and fixed point theorems combined with convex-power condensing operators.In our proofs,we do not need any hypothesis for the Banach space.Moreover,we don＇t also assume the resolvent is compact.Therefore our results improve and extend some known results in this field.A simple example is also given to illustrate our theory.

关 键 词：解析预解算子 CAPUTO分数阶导数 非紧测度 凸幂凝聚算子 温和解 

分 类 号：O175.12[理学—数学]