| 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)。 |
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| 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. |
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