Scholarlink

<p>In this article, we introduce a new operational matrix of the fractional-order derivative that depends on the Caputo operator of differentiation and first-kind Dickson polynomials. The established matrix, in addition to the Tau spectral method, will be used for solving three important applications in the fractional-order forms: the Bagley-Torvik problem, the Lane-Emden type equation, and Bratu’s problem. The primary approach for addressing these applications involves transforming the fractional-order problem and its conditions into a system of algebraic equations with unknown coefficients. The error estimation and convergence analysis of the proposed method will be thoroughly examined. Our proposed technique will be applied through some examples with comparisons. The introduced numerical results support the theoretical ones, in addition to demonstrating the accuracy and applicability of the suggested method.</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

Dickson polynomial-based solutions for fractional order physics problems

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年9月30日

查看全文
  • A. A. El-Sayed,
  • S. Boulaaras,
  • F. A. Al-Kharousi

摘要

In this article, we introduce a new operational matrix of the fractional-order derivative that depends on the Caputo operator of differentiation and first-kind Dickson polynomials. The established matrix, in addition to the Tau spectral method, will be used for solving three important applications in the fractional-order forms: the Bagley-Torvik problem, the Lane-Emden type equation, and Bratu’s problem. The primary approach for addressing these applications involves transforming the fractional-order problem and its conditions into a system of algebraic equations with unknown coefficients. The error estimation and convergence analysis of the proposed method will be thoroughly examined. Our proposed technique will be applied through some examples with comparisons. The introduced numerical results support the theoretical ones, in addition to demonstrating the accuracy and applicability of the suggested method.