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基于直接方法的非线性模糊偏微分方程的分数阶分析

Fractional analysis of non-linear fuzzy partial differential equations by using a direct procedure.

作者信息

Arshad Muhammad, Khan Shahbaz, Khan Hassan, Ali Hamid, Ali Ijaz

机构信息

Department of Mathematics, Abdul Wali Khan University, Mardan, Pakistan.

Department of Mathematics, Near East University TRNC, Mersin 10, Turkey.

出版信息

Sci Rep. 2024 Apr 26;14(1):9627. doi: 10.1038/s41598-024-60123-5.

DOI:10.1038/s41598-024-60123-5
PMID:38671024
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC11579456/
Abstract

In this study, an accurate analytical solution is presented for fuzzy FPDEs. It is done by using a novel method called the Laplace-residual power series (LRPSM) to build a series solution to the given problems. The fundamental instruments of the employed method are the Laplace transform, fractional Laurent, and fractional power series. Using the idea of a limit at infinity, we provide a series solution to a fuzzy FPDE with quick convergence and simple coefficient finding. We analyze three cases to obtain approximate and exact solutions to show the effectiveness and reliability of the Laplace- residual power series approach. To demonstrate the accuracy of the suggested procedure, we compare the findings to the real data.

摘要

在本研究中，给出了模糊分数阶偏微分方程（FPDEs）的精确解析解。这是通过使用一种名为拉普拉斯 - 残差幂级数（LRPSM）的新方法来构建给定问题的级数解实现的。所采用方法的基本工具是拉普拉斯变换、分数阶洛朗级数和分数幂级数。利用无穷远处极限的概念，我们为模糊分数阶偏微分方程提供了一个收敛快且系数求解简单的级数解。我们分析了三种情况以获得近似解和精确解，以展示拉普拉斯 - 残差幂级数方法的有效性和可靠性。为了证明所建议方法的准确性，我们将结果与实际数据进行了比较。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/833f/11579456/a84732e967d4/41598_2024_60123_Fig8_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/833f/11579456/016d11d209d2/41598_2024_60123_Fig1_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/833f/11579456/5526b9837f4a/41598_2024_60123_Fig2_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/833f/11579456/fc14b13797a5/41598_2024_60123_Fig3_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/833f/11579456/01832fc4a4f6/41598_2024_60123_Fig4_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/833f/11579456/1b8dea9d866f/41598_2024_60123_Fig5_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/833f/11579456/1a43db7bc6c7/41598_2024_60123_Fig6_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/833f/11579456/9bb1ddcb50fc/41598_2024_60123_Fig7_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/833f/11579456/a84732e967d4/41598_2024_60123_Fig8_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/833f/11579456/016d11d209d2/41598_2024_60123_Fig1_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/833f/11579456/5526b9837f4a/41598_2024_60123_Fig2_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/833f/11579456/fc14b13797a5/41598_2024_60123_Fig3_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/833f/11579456/01832fc4a4f6/41598_2024_60123_Fig4_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/833f/11579456/1b8dea9d866f/41598_2024_60123_Fig5_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/833f/11579456/1a43db7bc6c7/41598_2024_60123_Fig6_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/833f/11579456/9bb1ddcb50fc/41598_2024_60123_Fig7_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/833f/11579456/a84732e967d4/41598_2024_60123_Fig8_HTML.jpg

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