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关于Banach空间中涉及Caputo导数的分数阶微分方程解的存在性

On the existence of solutions to fractional differential equations involving Caputo -derivative in Banach spaces.

作者信息

Al-Shbeil Isra, Bouzid Houari, Abdelkader Benali, Lupas Alina Alp, Samei Mohammad Esmael, Alhefthi Reem K

机构信息

Department of Mathematics, Faculty of Sciences, The University of Jordan, 11942 Amman, Jordan.

Department of Mathematics, Faculty of Exact Science and Informatics, Hassiba Benbouali University of Chlef, Ouled Fares, Chlef 02000, Laboratory of Mathematics and Applications (LMA), Algeria.

出版信息

Heliyon. 2024 Dec 9;11(1):e40876. doi: 10.1016/j.heliyon.2024.e40876. eCollection 2025 Jan 15.

DOI:10.1016/j.heliyon.2024.e40876
PMID:39758380
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC11699369/
Abstract

The generalization of BVPs always covers a wide range of equations. Our choice in this research is the generalization of Caputo-type fractional discrete differential equations that include two or more fractional -integrals. We analyze the existence and uniqueness of solutions to the multi-point nonlinear BVPs base on fixed point theory, including fixed point theorem of Banach, Leray-nonlinear Schauder's alternative, and Leray-degree Schauder's theory. Finally, several examples are presented to demonstrate accuracy of our results.

摘要

边值问题（BVPs）的推广总是涵盖各种各样的方程。我们在本研究中的选择是对包含两个或更多分数阶积分的Caputo型分数阶离散微分方程进行推广。我们基于不动点理论分析多点非线性边值问题解的存在性和唯一性，包括巴拿赫不动点定理、勒雷 - 非线性绍德尔择一定理以及勒雷 - 度绍德尔理论。最后，给出几个例子以证明我们结果的准确性。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4322/11699369/2bad8ef60ad6/gr004.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4322/11699369/7969ce871ba6/gr001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4322/11699369/f86b36a8d95c/gr002.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4322/11699369/346bfa8286a3/gr003.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4322/11699369/2bad8ef60ad6/gr004.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4322/11699369/7969ce871ba6/gr001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4322/11699369/f86b36a8d95c/gr002.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4322/11699369/346bfa8286a3/gr003.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4322/11699369/2bad8ef60ad6/gr004.jpg

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本文引用的文献

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A fractional calculus approach to self-similar protein dynamics.一种用于自相似蛋白质动力学的分数阶微积分方法。
Biophys J. 1995 Jan;68(1):46-53. doi: 10.1016/S0006-3495(95)80157-8.