Failla Giuseppe, Zingales Massimiliano
Department of Civil, Environmental, Energy and Materials Engineering (DICEAM), University of Reggio Calabria, Via Graziella, Località Feo di Vito, 89124 Reggio Calabria, Italy.
Department of Engineering, University of Palermo, Viale delle Scienze ed. 8, 90128, Palermo, Italy.
Philos Trans A Math Phys Eng Sci. 2020 May 29;378(2172):20200050. doi: 10.1098/rsta.2020.0050. Epub 2020 May 11.
Fractional calculus is now a well-established tool in engineering science, with very promising applications in materials modelling. Indeed, several studies have shown that fractional operators can successfully describe complex long-memory and multiscale phenomena in materials, which can hardly be captured by standard mathematical approaches as, for instance, classical differential calculus. Furthermore, fractional calculus has recently proved to be an excellent framework for modelling non-conventional fractal and non-local media, opening valuable prospects on future engineered materials. The theme issue gathers cutting-edge theoretical, computational and experimental studies on advanced materials modelling via fractional calculus, with a focus on complex phenomena and non-conventional media. This article is part of the theme issue 'Advanced materials modelling via fractional calculus: challenges and perspectives'.
分数阶微积分如今已成为工程科学中一项成熟的工具，在材料建模方面有着非常广阔的应用前景。事实上，多项研究表明，分数阶算子能够成功描述材料中复杂的长记忆和多尺度现象，而这些现象很难用标准数学方法（如经典微分学）来捕捉。此外，分数阶微积分最近已被证明是一种用于对非常规分形和非局部介质进行建模的优秀框架，为未来的工程材料开辟了宝贵的前景。本专题汇集了关于通过分数阶微积分进行先进材料建模的前沿理论、计算和实验研究，重点关注复杂现象和非常规介质。本文是“通过分数阶微积分进行先进材料建模：挑战与展望”专题的一部分。
