Accurate relationships between fractals and fractional integrals: new approaches and evaluations

DOI10.1515/fca-2017-0066zbMath1374.28014OpenAlexW2768012029MaRDI QIDQ1677978

Iskander Gubaidullin, Raoul R. Nigmatullin, Wei Zhang

Publication date: 14 November 2017

Published in: Fractional Calculus \& Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/fca-2017-0066

zbMATH Keywords

Cantor setaveraging of smooth functions on spatial fractal setsfractal objectself-similar objectspatial fractional integral

Mathematics Subject Classification ID

Singular functions, Cantor functions, functions with other special properties (26A30) Fractional derivatives and integrals (26A33) Self-similar stochastic processes (60G18) Fractals (28A80) Hausdorff and packing measures (28A78)

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• A physically based connection between fractional calculus and fractal geometry
• Local fractional similarity solution for the diffusion equation defined on Cantor sets
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• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• Fractal calculus involving gauge function
• New relationships connecting a class of fractal objects and fractional integrals in space

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