一类分数阶差分方程的初值问题  

Initial Value Problem of a Class of Fractional Difference Equations

作　　者：李晓艳[1] 刘松[1] 蒋威[1] 

机构地区：[1]安徽大学数学科学学院,合肥230601

出　　处：《工程数学学报》2013年第6期881-889,共9页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(11071001);教育部博士点基金(20093401110001);安徽大学博士科研启动基金(023033190249);安徽大学青年科学基金(02303050055)~~

摘　　要：许多物理、航天科学、生态科学、工程中的实际问题都需要用分数阶差分方程来描述,因此对分数阶差分方程的研究有着十分重要的理论意义和实践价值.本文利用分数阶差分与和分性质,分两种情况给出了一类非线性项含有未知函数差分的分数阶差分方程解的表达式.进而,运用解的表达式及压缩映像原理,得到了这类分数阶差分方程解的存在唯一性条件.最后,给出具体例子验证定理的有关结果.Many practical problems, such as those from physics, aerospace science, ecological science, engineering and so on, need to be described by fractional discrete equations, so it is important in theory and practical significance to study these equations. In this paper, by uti- lizing properties of discrete fractional calculus, the explicit solutions for the fractional discrete equations in which nonlinear terms contain fractional difference of unknown functions are given in two cases. At the same time, we obtain the conditions for the existence and uniqueness of solutions by using the expression of solutions and the Banach contraction mapping principle. Finally, we give an example to verify theoretical results.

关 键 词：分数阶差分与和分 分数阶差分方程 解的存在唯一性 

分 类 号：O175.14[理学—数学]