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《Chinese Journal of Engineering Mathematics》 2013-06
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Initial Value Problem of a Class of Fractional Difference Equations

LI Xiao-Yan;LIU Song;JIANG Wei;School of Mathematical Sciences,Anhui University;  
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 utilizing 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.
【Fund】: 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)~~
【CateGory Index】: O175.7
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