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arXiv · 2302.12642

The Mellin Transform and Non-local Derivatives of Fractal Calculus

Alireza Khalili Golmankhaneh·Kerri Welch·Cristina Serpa·Palle E. T. Jørgensen
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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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Alireza Khalili Golmankhaneh, Kerri Welch, Cristina Serpa, Palle E. T. Jørgensen. 2023-02-19. The Mellin Transform and Non-local Derivatives of Fractal Calculus. https://arxiv.org/abs/2302.12642

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