分形Mellin变换与非局部导数

Pub Date : 2023-11-19 DOI:10.1515/gmj-2023-2094
Alireza Khalili Golmankhaneh, Kerri Welch, Cristina Serpa, Palle E. T. Jørgensen
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引用次数: 0

摘要

本文对分形集的分形演算与分形曲线的分形演算进行了比较。介绍了分形曲线的Riemann-Liouville积分和Caputo积分及其导数的类似形式,它们都是非局部导数。此外,还定义了分形曲线上分形非局部微分方程的类似分数阶拉普拉斯算子的概念。此外,本文还介绍了分形局部Mellin变换和分形非局部变换作为求解分形微分方程的工具。结果与表格和例子支持,以证明研究结果。
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Fractal Mellin transform and non-local derivatives
Abstract This paper provides a comparison between the fractal calculus of fractal sets and fractal curves. There are introduced the analogues of the Riemann–Liouville and Caputo integrals and derivatives for fractal curves, which are non-local derivatives. Moreover, the concepts analogous to the fractional Laplace operator to address fractal non-local differential equations on fractal curves are defined. Additionally, in the paper it is introduced the fractal local Mellin transform and fractal non-local transform as tools for solving fractal differential equations. The results are supported with tables and examples to demonstrate the findings.
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