序列型分数阶差分方程解的存在唯一性  

The existence and uniqueness of the solutions for sequential fractional difference equations

作　　者：李小敏 惠小健[1] LI Xiaomin;XI Xiaojian(Faculty of science,Xijing University,Xi’an 710123,China)

机构地区：[1]西京学院理学院,西安710123

出　　处：《扬州大学学报（自然科学版）》2021年第6期21-25,共5页Journal of Yangzhou University：Natural Science Edition

基　　金：陕西省自然科学基础研究计划资助项目(2020JM-646);西京学院校级基金资助项目(XJ190206).

摘　　要：以向前差分为出发点,研究序列型分数阶线性及非线性差分方程解的存在唯一性.通过给出向前序列型分数阶差分的定义以及基于向前差分的Z变换公式,利用Z变换、数学归纳法及Mittag-Leffler函数得到序列型分数阶差分方程解的存在性,并通过逆Z变换及零次近似得到了差分方程解的唯一性.Taking forward difference as a starting point, the existence and uniqueness of solutions for sequential fractional linear and nonlinear difference equations are studied. Firstly, the definition of the forward sequence fractional-order difference and the Z transform formula based on the forward difference are given. Secondly, the existence of the solution of the sequence fractional-order difference equation is obtained by using the Z transform, mathematical induction and mittag-leffler function. Finally, the uniqueness of the solution of the difference equation is obtained by the inverse Z transform and the zero-order approximation.

关 键 词：序列型分数阶 差分方程 Z变换 

分 类 号：O175.7[理学—数学]