Scholarlink

<p>This paper investigates the theoretical foundations of Bessel fractional calculus. Distinctions are established between Bessel fractional operators and their classical counterparts. Semigroup theory is developed for the Bessel fractional integral operator, showing that it generates a <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(C_{0}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>C</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation>-semigroup under specific conditions. Fundamental connections between differential and integral operators are analyzed, with comparisons drawn to classical theory. Furthermore, the structure of the solution space for homogeneous fractional differential equations is characterized. The influence of operator parameters–specifically the order and Bessel index <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\nu \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ν</mi> </math></EquationSource> </InlineEquation> on the resulting integral/differential operations is examined.</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

Bessel fractional calculus operators: perspective via Gaussian hypergeometric function

  • 期刊论文

  • 发表日期：

    2026年7月1日

查看全文
  • Zhengzhi Lu

摘要

This paper investigates the theoretical foundations of Bessel fractional calculus. Distinctions are established between Bessel fractional operators and their classical counterparts. Semigroup theory is developed for the Bessel fractional integral operator, showing that it generates a \(C_{0}\) C 0 -semigroup under specific conditions. Fundamental connections between differential and integral operators are analyzed, with comparisons drawn to classical theory. Furthermore, the structure of the solution space for homogeneous fractional differential equations is characterized. The influence of operator parameters–specifically the order and Bessel index \(\nu \) ν on the resulting integral/differential operations is examined.