A fractional model for insulation clothings with cocoon-like porous structure

Both silk worm co coons and wild silk worm co coons have ex cel lent me chan i cal prop er ties, as a pro tec tive bar rier against en vi ron men tal dam age and at tack by nat u ral pred a tors. In par tic u lar, this multilayer po rous struc ture can be ex cep tion ally tough to en hance the chance of sur vival for pu pas while sup port ing their met a bolic ac tiv ity. Here, a frac tional de riv a tive is de fined through the variational it er a tion method, and its ap pli ca tion to ex plain ing the out stand ing ther mal pro tec tion of in su la tion clothings with co coon-like po rous struc ture is elu ci dated. The fractal hi er ar chic struc ture of in su la tion clothings makes hu man body math e mat i cally adapted for ex treme tem per a ture en vi ron ment.