文章摘要
张晓锐,王良龙.一类分数阶混合型差分与和分方程任意初值问题解 的存在唯一性[J].安徽建筑大学学报,2020,28(1):83-86
一类分数阶混合型差分与和分方程任意初值问题解 的存在唯一性
Existence and Uniqueness of the Solution of the Initial ValueProblems for a Class of Riemann-Loiuville Fractional MixedDifference and Summation Equations
  
DOI:10.11921/j.issn.2095-8382.20200114
中文关键词: 分数阶差分和分方程  初值问题  Volterra 和分方程  Mittag-Leffler 函数  Gronwall 不等式
英文关键词: fractional difference and summation equation,initial value problem  volterra summation equation  mittag-leffler functions  discrete fractional gronwall inequality  existence and uniqueness of solutions
基金项目:国家自然科学基金(11771001);安徽省质量工程项目(2018zygc107)。
作者单位
张晓锐 安徽大学数学科学学院合肥230039 
王良龙 安徽大学数学科学学院合肥230039 
摘要点击次数: 481
全文下载次数: 0
中文摘要:
      本文研究一类Riemann-Liouville 型混合分数阶差分与和分方程的初值问题,通过建立与该类初值问 题解等价的Volterra 和分方程,运用Banach 压缩映射原理,在一定条件下,证明该初值问题解的存在唯一 性. 另外,还通过构造逐次迭代序列,运用离散Mittag-Leffler 函数的性质和离散分数阶Gronwall 不等式, 在较弱的条件下得到该初值问题解的存在唯一性。
英文摘要:
      This paper is concerned with the initial value problems for a class of Riemann-Loiuville fractional equations mixed with difference and summation. By establishing the Volterra Summation equation equivalent to the solution of this kind of initial value problem,the existence and uniqueness of the solutions of the initial value problem are proved under certain conditions by using the principle of Banach Compression Mapping. In addition,the existence and uniqueness of solutions of the initial value problem is also obtained under weak conditions by using the successive approximation method combined with the discrete Mittag-Leffler function and the discrete fractional Gronwall inequality.
查看全文   查看/发表评论  下载PDF阅读器
关闭

分享按钮