Existence theory for nabla fractional three-point boundary value problems via continuation methods for contractive maps

IF 0.7 4区 数学 Q2 MATHEMATICS Topological Methods in Nonlinear Analysis Pub Date : 2023-07-16 DOI:10.12775/tmna.2022.043
J. Jonnalagadda
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引用次数: 0

Abstract

In this article, we analyse an $\alpha$-th order, $1 < \alpha \leq 2$, nabla fractional three-point boundary value problem (BVP). We construct the Green's function associated to this problem and derive a few of its important properties. We then establish sufficient conditions on existence and uniqueness of solutions for the corresponding nonlinear BVP using the modern ideas of continuation methods for contractive maps. Our results extend recent results on nabla fractional BVPs. Finally, we provide an example to illustrate the applicability of main results.
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压缩映射的延拓法求解nabla分数点边值问题的存在性理论
在本文中,我们分析了一个$\alpha$ -阶,$1 < \alpha \leq 2$, nabla分数三点边值问题(BVP)。我们构造了与这个问题相关的格林函数,并推导了它的一些重要性质。然后利用现代压缩映射的延拓方法思想,建立了相应非线性BVP解存在唯一性的充分条件。我们的结果扩展了最近关于分数bvp的结果。最后,通过一个算例说明了主要结果的适用性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
1.00
自引率
0.00%
发文量
57
审稿时长
>12 weeks
期刊介绍: Topological Methods in Nonlinear Analysis (TMNA) publishes research and survey papers on a wide range of nonlinear analysis, giving preference to those that employ topological methods. Papers in topology that are of interest in the treatment of nonlinear problems may also be included.
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