Open AccessTwo-scale mathematics and fractional calculus for thermodynamics
Author(s) -
JiHuan He,
Fei-Yu Ji
Publication year - 2019
Publication title -
thermal science/thermal science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.339
H-Index - 43
eISSN - 2334-7163
pISSN - 0354-9836
DOI - 10.2298/tsci1904131h
Subject(s) - calculus (dental) , fractional calculus , scale (ratio) , time scale calculus , fractal , mathematics , multivariable calculus , mathematical analysis , physics , medicine , dentistry , quantum mechanics , control engineering , engineering
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.