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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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【Co-citations】
Chinese Journal Full-text Database 7 Hits
1 ZHAO Xiao-hong;KANG Shu-gui;GAO Ying;School of Mathematical and Computer Sciences,Shanxi Normal University;School of Mathematical and Computer Sciences,Shanxi Datong University;;Existence and Uniqueness of Solution to A Coupled System of Fractional Difference Equations with Nonlocal Conditions[J];Journal of Biomathematics;2013-02
2 ZHANG Xiao-na;HU Wei-min;QIU Zhong-wei;School of Mathematics and Statistics,Ili Normal University;;Mutiple Positive Solution of Fractional Differential Equation Boundary Value Problem[J];Journal of Biomathematics;2013-03
3 CHEN Hui-qin;KANG Shu-gui;GUO Jian-min;School of Mathematics and Computer Sciences,Datong University;;Existence and Uniqueness of Solutions about Fractional Difference Equation with Nonlocal Conditions[J];Mathematics in Practice and Theory;2013-19
4 HUANG Juan-Juan;HAN Xiao-Ling;GAO Cheng-Hua;College of Mathematics and Information Science,Northwest Normal University;;The existence of solutions for the boundary value problem of fractional hybrid difference equation[J];Journal of Sichuan University(Natural Science Edition);2013-06
5 GUO Caixia;GUO Jianmin;KANG Shugui;LI Huapeng;School of Mathematics and Computer Sciences,Shanxi Datong University;;On a Caputo fractional boundary value problem for fractional boundary conditions[J];Journal of Yanbian University(Natural Science Edition);2013-03
6 Yu Zhang;Chengmin Hou;Dept.of Math.,Yanbian University;;ON DISCRETE SEQUENTIAL FRACTIONAL BOUNDARY VALUE PROBLEM WITH FRACTIONAL BOUNDARY CONDITIONS[J];微分方程年刊(英文版);2013-03
7 MENG Xian-qing;CHEN Hui-qin;School of Mathematics and Computer Sciences,Shanxi Datong University;;Existence and Uniqueness of Solutions about Caputo Fractional Difference Equation with Nonlocal Conditions[J];Journal of Shanxi Datong University(Natural Science Edition);2013-05
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