一类非线性分数阶微分方程边值问题的稳定单调迭代解

Journal of Nonlinear Sciences and Applications Pub Date : 2019-01-30 DOI:10.22436/JNSA.012.06.04

Sajjad Ali, M. Arif, Durdana Lateef, M. Akram

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引用次数: 4

摘要

构造了非线性分数阶微分方程边值问题极值解存在的充分条件。将上下解法与单调迭代技术相结合，构造了所考虑问题的迭代解的充分条件。探讨了有关Hyers-Ulam型稳定性的一些适当结果。在此基础上，构造了问题的最小解和最大解。我们还构造并给出了最大误差估计，并通过两个例子验证了所得到的结果。

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Stable monotone iterative solutions to a class of boundary value problems of nonlinear fractional order differential equations

We construct sufficient conditions for existence of extremal solutions to boundary value problem (BVP) of nonlinear fractional order differential equations (NFDEs). By combing the method of lower and upper solution with the monotone iterative technique, we construct sufficient conditions for the iterative solutions to the problem under consideration. Some proper results related to Hyers-Ulam type stability are investigated. Base on the proposed method, we construct minimal and maximal solutions for the proposed problem. We also construct and provide maximum error estimates and test the obtain results by two examples.

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来源期刊

Journal of Nonlinear Sciences and Applications MATHEMATICS, APPLIED-MATHEMATICS

自引率

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发文量

期刊介绍： The Journal of Nonlinear Science and Applications (JNSA) (print: ISSN 2008-1898 online: ISSN 2008-1901) is an international journal which provides very fast publication of original research papers in the fields of nonlinear analysis. Journal of Nonlinear Science and Applications is a journal that aims to unite and stimulate mathematical research community. It publishes original research papers and survey articles on all areas of nonlinear analysis and theoretical applied nonlinear analysis. All articles are fully refereed and are judged by their contribution to advancing the state of the science of mathematics. Manuscripts are invited from academicians, research students, and scientists for publication consideration. Papers are accepted for editorial consideration through online submission with the understanding that they have not been published, submitted or accepted for publication elsewhere.