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Updated: Dec 21, 2025
08:23
Finite Element Modelling of a Cellular Electric Microenvironment
Published on: May 18, 2021
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Advanced materials modelling via fractional calculus: challenges and perspectives.
Giuseppe Failla1, Massimiliano Zingales2
1Department of Civil, Environmental, Energy and Materials Engineering (DICEAM), University of Reggio Calabria, Via Graziella, Località Feo di Vito, 89124 Reggio Calabria, Italy.
Summary
Fractional calculus effectively models complex material behaviors like long memory and multiscale phenomena. This advanced mathematical approach offers new insights for designing novel engineered materials with fractal and non-local properties.
Area of Science:
- Engineering Science
- Materials Science
- Applied Mathematics
Background:
- Fractional calculus is a powerful tool for describing complex phenomena in materials.
- Standard mathematical methods struggle with long-memory and multiscale behaviors.
- Fractional operators offer a superior approach for these challenges.
Purpose of the Study:
- To explore advanced materials modeling using fractional calculus.
- To highlight applications in complex phenomena and non-conventional media.
- To present cutting-edge theoretical, computational, and experimental studies.
Main Methods:
- Application of fractional operators to materials modeling.
- Utilizing fractional calculus for fractal and non-local media.
- Integration of theoretical, computational, and experimental approaches.
Main Results:
- Fractional calculus successfully captures long-memory and multiscale material phenomena.
- Demonstrated effectiveness in modeling non-conventional fractal and non-local media.
- Opened new avenues for engineered materials design.
Conclusions:
- Fractional calculus is a key enabler for advanced materials modeling.
- It provides essential tools for understanding complex material behaviors.
- Future engineered materials will benefit from these advanced mathematical frameworks.
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