Scholarlink

<p>The Cauchy problem for an evolution equation with a fractional derivative and a strongly positive operator coefficient in Banach space is considered. The exact solution to the problem is represented as a series in terms of the Cayley transform of the operator coefficient and the Laguerre–Cayley polynomials. A partial sum of this series is used to construct an approximate solution. Estimates of the error of such an approximation are obtained, indicating an exponential rate of convergence for the proposed method. The theoretical results are illustrated by numerical examples.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Exponentially Convergent Method for Solving a Fractional-Order Evolution Equation in a Banach Space

  • 期刊论文

  • 发表日期：

    2026年3月1日

查看全文
  • V. L. Makarov,
  • N. V. Mayko,
  • V. L. Ryabichev

摘要

The Cauchy problem for an evolution equation with a fractional derivative and a strongly positive operator coefficient in Banach space is considered. The exact solution to the problem is represented as a series in terms of the Cayley transform of the operator coefficient and the Laguerre–Cayley polynomials. A partial sum of this series is used to construct an approximate solution. Estimates of the error of such an approximation are obtained, indicating an exponential rate of convergence for the proposed method. The theoretical results are illustrated by numerical examples.