mriselMagnetic Resonance in SolidsMagnetic Resonance in Solids2072-5981Kazan Federal University10.26907/mrsej-24105mrisel-244Research ArticleСтатьиFractals and fractional integrals: Are there some accurate relationships between them?NigmatullinR. R.

Kazan 420111

renigmat@gmail.comKazan National Research Technical University (KAI)Russian Federation202419042024261SPECIAL ISSUE dedicated to Boris I. Kochelaev's 90th birthday24105 (14 pp.)Copyright © Nigmatullin R.R., 20242024Nigmatullin R.R.Nigmatullin R.R.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://www.mrsej.ru/jour/article/view/244

This study establishes precise links between the fractional integral of the RL-type and the averaging technique of a smooth function over 1D-fractal sets. These findings were previously reported in the works [1], [2]. To draw in the interest of other experts operating in the NMR/EPR zones, it is helpful to repeat them again. The physical meaning of these acquired formulas is explained and numerical verifications are performed with the purpose of confirming the analytical results. Furthermore, results were achieved for a combination of fractal circuits with a discrete set of fractal dimensions that were generalized. We suppose that these new results help understand deeper the intimate links between fractals and fractional integrals of different types, especially in applications of the fractional operators in complex systems.

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The authors declare that there are no conflicts of interest present.