TY - JOUR
TI - Two-scale mathematics and fractional calculus for thermodynamics
AU - He Ji-Huan
AU - Ji Fei-Yu
JN - Thermal Science
PY - 2019
VL - 23
IS - 4
SP - 2131
EP - 2133
PT - Article
AB - 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.