Two-scale mathematics and fractional calculus for thermodynamics

作者：Ji‐Huan He, Fei-Yu Ji · 发表于：Thermal Science · 年份：2019 · DOI：10.2298/tsci1904131h · 被引用次数：298 · 研究领域：Fractional Differential Equations Solutions、Statistical Mechanics and Entropy、Advanced Thermodynamics and Statistical Mechanics

A three dimensional problem can be approximated by either a two-dimensional or one-dimensional case, but some information will be lost. To reveal the lost information due to the lower dimensional approach, two-scale mathematics is needed. Generally one scale is established by usage where traditional calculus works, and the other scale is for revealing the lost information where the continuum assumption might be forbidden, and fractional calculus or fractal calculus has to be used. The two-scale transform can approximately convert the fractional calculus into its traditional partner, making the two-scale thermodynamics much promising.