分数阶微分方程初值问题解的存在性与唯一性  

On the Existence and Uniqueness of Solutions for Initial Value Problem of Fractional Differential Equations

作　　者：李秋萍[1] 孙书荣[1] 张萌[1] 赵以阁[1] 

机构地区：[1]济南大学理学院,山东济南250022

出　　处：《济南大学学报（自然科学版）》2010年第3期312-315,共4页Journal of University of Jinan(Science and Technology)

基　　金：国家自然科学基金(60774004);山东省自然科学基金(Y2007A27;Y2008A28);济南大学博士基金(B0621;XBS0843)

摘　　要：运用Banach压缩映射原理的推论和广义Lipschitz条件，研究一类阶数在1～2范围内的分数阶微分方程初值问题解的存在性与唯一性，给出该问题存在唯一解的充分条件，推广已有某些结果。By using the Banach contraction mapping principle of corollary and generalized Lipschitz conditions,we consider the existence and uniqueness of solution of the initial value problem for a class of fractional differential equations which order within 1 to 2. Sufficient conditions are obtained for the existence and uniqueness of one solution of the problem. Some results in this paper extend the results given in literatures.

关 键 词：分数阶微分方程 Riemann-Liouville分数阶导数 初值问题 BANACH压缩映射原理 

分 类 号：O175[理学—数学]