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分数阶微分差分方程解的存在性与唯一性

Existence and uniqueness of solutions for Fractional Differential Difference Equations

中文摘要英文摘要

从一类分数阶微分差分方程边值问题的近似解出发,应用Picard's 迭代方法研究证明了其边值问题解的迭代序列所满足的形式及其存在唯一解的充要条件;讨论了这类边值问题不考虑近似解以及非Lipschitz类因素时,其一般解的存在条件;最后通过一个数值算例验证了这类边值问题解的存在性以及解与其迭代序列的误差估计.

From a class of fractional order differential difference equation boundary value problem of approximate solution of and application Picard's iteration methods of proved satisfied by the iterative sequence of the solutions of boundary value problems of the form and existence and uniqueness of the solution of necessary and sufficient conditions are discussed. The boundary value problem without considering approximate solution and non Lipschitz class factors, the conditions for the existence of the general solutions. Finally, a numerical examples show that this kind of solution for boundary value problem of existence and the solution and the iterative sequence of error estimation.

孙宇锋、曾广钊、王兆顺、屈威

数学

分数阶微分差分方程迭代算法近似解误差估计

fractional differential difference equationiterative algorithmapproximate solutionestimation of error

孙宇锋,曾广钊,王兆顺,屈威.分数阶微分差分方程解的存在性与唯一性[EB/OL].(2015-06-29)[2025-08-16].http://www.paper.edu.cn/releasepaper/content/201506-353.点此复制

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