探索分数-整微分方程与无限延迟的非局部合系统的动态
Khalid K Ali1, K R Raslan1, Amira Abd-Elall Ibrahim2
1Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr-City, Cairo, Egypt.
Heliyon
|July 23, 2024
概括
本研究研究了配对的分数整微分方程与无限延迟. 我们确定了解决方案的存在,独特性和持续依赖性,并展示了这些复杂系统的数值方法.
科学领域:
- 应用数学 应用数学 应用数学
- 分数微积分的计算.
- 微分方程 微分方程 微分方程
背景情况:
- 分数整微分方程模型复杂的现象.
- 具有无限延迟和非局部条件的系统存在独特的挑战.
- 卡普托和法布里齐奥运算子的新定义增强了数学建模.
研究的目的:
- 分析分数整微分方程系统的解决方案的存在,独特性和连续依赖性.
- 引入和应用Caputo和Fabrizio差分运算符的新定义.
- 用有限-形方法数量解决拟议的系统.
主要方法:
- 严格的数学分析来证明解决方案的存在和独特性.
- 对初始条件和参数的持续依赖性的研究.
- 应用有限形方法进行数值近似.
主要成果:
- 解决方案的存在和独特性被严格确立.
- 证明了解决方案的持续依赖.
- 有限梯形方法在解决分数系统方面证明是有效的.
结论:
- 该研究提供了一个复杂的分数系统的全面分析.
- 这些发现有助于理论理解和分数整微分方程的数值解.
- 这项研究在各种科学和工程领域都有潜在的应用.
相关概念视频
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