使用Tau Legendre算法对Hilfer (α,β) 框架集的延迟微分模型的分数系统进行正确位置分析和伪Galerkin近似
Hind Sweis1, Omar Abu Arqub2, Nabil Shawagfeh3
1Department of Data Science, Faculty of Data Science, Arab American University, Ramallah, Palestine.
PloS one
|June 25, 2024
概括
本研究探讨了用于建模复杂系统的分数计算,使用希尔弗框架进行理论分析和加勒金算法进行分数延迟微分方程的数值解.
科学领域:
- 数学 数学 是一个数学.
- 应用数学 应用数学 应用数学
- 数字分析 数字分析
背景情况:
- 分数计算为模拟复杂系统提供了先进的方法.
- 延迟微分方程 (DDE) 对具有时间延迟的系统至关重要.
- 解决分数DDE的现有方法存在局限性.
研究的目的:
- 从理论和数值上分析一个分数延迟微分方程 (DFDE) 系统.
- 使用希尔弗 (α,β) 框架来确定解决方案的存在和独特性 (EUE).
- 开发和验证一个有效的数值算法来解决这些系统.
主要方法:
- 使用希尔弗 (α,β) 框架和分数运算符 (FRD,FCD,FHD) 的属性进行理论分析.
- 使用考希矩阵定理 (CMT) 将分数延迟系统转换为等效分数伏尔特拉积分方程 (FVIEs).
- 数值分析采用加勒金算法与直角转移的列德多项式 (OSLPs) 作为基础函数,在 MATHEMATICA 11 中实现.
主要成果:
- 理论上确立了DFDE解决方案的存在和独特性.
- 加勒金算法有效地将DFDE转换为数值估计的代数方程系统.
- 该数值算法与其他方法相比,在较少的代过程中显示出高精度,通过线性和非线性应用验证.
结论:
- 分数计算为建模和控制复杂系统提供了一个强大的框架.
- 提出的理论和数值方法为解决DFDE提供了有效和高效的方法.
- 该研究强调了在高级分数计算应用中进一步研究的潜力.
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