The Mellin Transform and Non-local Derivatives of Fractal Calculus

2023/02/19 by Alireza Khalili Golmankhaneh, Kerri Welch, Golmankhaneh, Alireza Khalili +5
Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #FOS: Mathematics #General Mathematics (math.GM) #Mathematical Dynamics and Fractals #Statistical Mechanics and Entropy

paper · pdf · doi:10.48550/arxiv.2302.12642

openalex publication_date 2023/02/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, the fractal calculus of fractal sets and fractal curves are compared. The analogues of the Riemann-Liouville and the Caputo integrals and derivatives are defined for the fractal curves which are non-local derivatives. The analogous for the fractional Laplace concepts are defined to solve fractal non-local differential equations on fractal curves. The fractal local Mellin and fractal non-local transforms are defined to solve fractal differential equations. We present tables and examples to illustrate the results.

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