![]() The applications will involve a wide variety of fractional operators, with a constant order as well as variable one the interest in fractional operators of variable order is growing in the recent literature, as valuable tools to model evolutionary phenomena without changing the governing equations.Ģ. Material hereditariness: viscoelasticity Understanding the complex behaviour of materials and modelling non-conventional media are, perhaps, the most fascinating and increasingly relevant applications of fractional calculus, whose potential impact on materials science and engineering has to be fully investigated.Īlthough an exhaustive description of all aspects of fractional calculus applications to materials modelling is almost prohibitive, this theme issue will attempt to provide a broad perspective on the state of the art and most recent developments, with 14 papers on viscoelasticity, heat conduction and diffusion in porous media, non-local continua and fractal media. ![]() fractal and non-local ones, opening unexpected opportunities in the design of new materials. ![]() On the other hand, fractional calculus has provided a consistent framework to model non-conventional media, e.g. Indeed, power-law dependence of fractional operators has proved ideally suitable to model non-local behaviour of materials in time or space, which plays a crucial role in several phenomena but cannot be captured by standard mathematical approaches as, for instance, classical differential calculus in this context, fractional operators have been fruitfully applied to describe challenging phenomena such as viscoelasticity, heat conduction, diffusion in porous media and wave propagation. The relevance of fractional calculus in applied science has progressively grown in recent years and, now, a considerable number of studies have definitely unveiled its potential to address several problems, especially in materials science and engineering. įor a long time, however, fractional calculus was regarded as an elegant yet purely theoretical field of mathematics, with limited practical use. Moving from the celebrated letter of De L'Hospital to Leibniz in 1695, discussing the concept of derivative of order ½, the mathematical bases of fractional differentiation and fractional integration were set by prominent mathematicians such as Liouville, Grünwald, Letnikov, Riesz, Caputo and many others up to recent times. Fractional operators may be considered as integro-differential operators of the convolution type with hypersingular power-law kernels.
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