Scholarlink

<p>In this paper, based on the notion of the operator of complex fractional derivative proposed by P. Závada [Commun. Math. Phys. 192 (1998), pp.261-285], we introduce a new class of fractional differential equations in the complex plane which allows the complex constant delay. By virtue of classifying the curvilinear cuts, the corresponding integral representations for the fractional differential equations are obtained under the effective integral paths. Meanwhile, the trajectories of the motion paths of the complex constant delays along all types of branch cuts in the complex plane are characterized. We demonstrate that not all branch cuts are suitable for discussing the complex delay fractional differential equations and analyze the geometric paths of these branch cuts in which the effective paths can be selected under our established sufficient conditions. Based on it, the existence, uniqueness and continuation theorems of complex delay fractional differential equations are established along the directions of the curvilinear cuts.</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

Fractional differential equations via Fourier transform and curvilinear cuts in the complex plane

  • 期刊论文

  • 发表日期：

    2025年11月11日

查看全文
  • Zhien Li,
  • Chao Wang,
  • Li Yang

摘要

In this paper, based on the notion of the operator of complex fractional derivative proposed by P. Závada [Commun. Math. Phys. 192 (1998), pp.261-285], we introduce a new class of fractional differential equations in the complex plane which allows the complex constant delay. By virtue of classifying the curvilinear cuts, the corresponding integral representations for the fractional differential equations are obtained under the effective integral paths. Meanwhile, the trajectories of the motion paths of the complex constant delays along all types of branch cuts in the complex plane are characterized. We demonstrate that not all branch cuts are suitable for discussing the complex delay fractional differential equations and analyze the geometric paths of these branch cuts in which the effective paths can be selected under our established sufficient conditions. Based on it, the existence, uniqueness and continuation theorems of complex delay fractional differential equations are established along the directions of the curvilinear cuts.