Scholarlink

<p>This paper provides a general framework for fractional calculus in two dimensions using the ideas of Sonin kernels and transmutation operators. We introduced the Riemann–Liouville fractional integral and its associated fractional derivatives in two dimensions, along with their key properties, including commutativity, semigroup laws, and the fundamental theorems of fractional calculus. Furthermore, we present several special cases of the transmutation, including left-shifted operators, fractional calculus with respect to a function, weighted fractional calculus, and weighted fractional calculus with respect to a function. The proposed theory generalizes many existing one-dimensional models and offers a flexible structure that can be extended to higher dimensions using the recent development of Sonin kernels in arbitrary dimensions and transmutation relations.</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

Transmuted fractional calculus with Sonin Kernels in two dimensions

  • 期刊论文

  • 发表日期：

    2026年3月3日

查看全文
  • Jaivee J. Gohil,
  • Krunal B. Kachhia

摘要

This paper provides a general framework for fractional calculus in two dimensions using the ideas of Sonin kernels and transmutation operators. We introduced the Riemann–Liouville fractional integral and its associated fractional derivatives in two dimensions, along with their key properties, including commutativity, semigroup laws, and the fundamental theorems of fractional calculus. Furthermore, we present several special cases of the transmutation, including left-shifted operators, fractional calculus with respect to a function, weighted fractional calculus, and weighted fractional calculus with respect to a function. The proposed theory generalizes many existing one-dimensional models and offers a flexible structure that can be extended to higher dimensions using the recent development of Sonin kernels in arbitrary dimensions and transmutation relations.