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通过广义卡普托-阿坦加纳-巴莱亚努导数求解分数阶朗之万-施图姆-刘维尔问题的高效结果。

Efficient results on fractional Langevin-Sturm-Liouville problem via generalized Caputo-Atangana-Baleanu derivatives.

作者信息

Thabet Sabri T M, Boutiara Abdelatif, Samei Mohammad Esmael, Kedim Imed, Vivas-Cortez Miguel

机构信息

Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Saveetha University, Chennai, Tamil Nadu, India.

Department of Mathematics, Radfan University College, University of Lahej, Lahej, Yemen.

出版信息

PLoS One. 2024 Oct 2;19(10):e0311141. doi: 10.1371/journal.pone.0311141. eCollection 2024.

DOI:10.1371/journal.pone.0311141
PMID:39356680
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC11446445/
Abstract

In this paper, we investigate the generalized Langevin-Sturm-Liouville differential problems involving Caputo-Atangana-Baleanu fractional derivatives of higher orders with respect to another positive, increasing function denoted by ρ. The fixed point theorems in the framework of Kransnoselskii and Banach are utilized to discuss the existence and uniqueness of the results. In addition, the stability criteria of Ulam-Hyers, generalize Ulam-Hyers, Ulam-Hyers-Rassias, and generalize Ulam-Hyers-Rassias are investigated by non-linear analysis besides fractional calculus. Finally, illustrative examples are reinforced by tables and graphics to describe the main achievements.

摘要

在本文中，我们研究了涉及关于另一个由ρ表示的正的递增函数的高阶Caputo-Atangana-Baleanu分数阶导数的广义Langevin-Sturm-Liouville微分问题。利用Kransnoselskii和Banach框架下的不动点定理来讨论结果的存在性和唯一性。此外，除了分数阶微积分外，还通过非线性分析研究了Ulam-Hyers稳定性准则、广义Ulam-Hyers稳定性准则、Ulam-Hyers-Rassias稳定性准则和广义Ulam-Hyers-Rassias稳定性准则。最后，通过表格和图形加强了示例说明以描述主要成果。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/31c4/11446445/19a8a30f2e0d/pone.0311141.g013.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/31c4/11446445/7ed0411c8cac/pone.0311141.g001.jpg
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https://cdn.ncbi.nlm.nih.gov/pmc/blobs/31c4/11446445/7b1cb6bef542/pone.0311141.g006.jpg
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https://cdn.ncbi.nlm.nih.gov/pmc/blobs/31c4/11446445/dc158507a681/pone.0311141.g008.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/31c4/11446445/5002f75a2c3e/pone.0311141.g009.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/31c4/11446445/abb095f07241/pone.0311141.g010.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/31c4/11446445/8ab2874531b2/pone.0311141.g011.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/31c4/11446445/87e49b33950b/pone.0311141.g012.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/31c4/11446445/19a8a30f2e0d/pone.0311141.g013.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/31c4/11446445/7ed0411c8cac/pone.0311141.g001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/31c4/11446445/808e59314440/pone.0311141.g002.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/31c4/11446445/1d318138e285/pone.0311141.g003.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/31c4/11446445/d262b3e8ffb2/pone.0311141.g004.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/31c4/11446445/ee84b1773dff/pone.0311141.g005.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/31c4/11446445/7b1cb6bef542/pone.0311141.g006.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/31c4/11446445/be67aa1c7621/pone.0311141.g007.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/31c4/11446445/dc158507a681/pone.0311141.g008.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/31c4/11446445/5002f75a2c3e/pone.0311141.g009.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/31c4/11446445/abb095f07241/pone.0311141.g010.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/31c4/11446445/8ab2874531b2/pone.0311141.g011.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/31c4/11446445/87e49b33950b/pone.0311141.g012.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/31c4/11446445/19a8a30f2e0d/pone.0311141.g013.jpg

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本文引用的文献

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2
On new common fixed point theorems via bipolar fuzzy [Formula: see text]-metric space with their applications.基于双极模糊 [Formula: see text]-度量空间的新公共不动点定理及其应用。
PLoS One. 2024 Jun 25;19(6):e0305316. doi: 10.1371/journal.pone.0305316. eCollection 2024.