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

Both silkworm cocoons and wild silkworm cocoons have excellent mechanical properties, as a protective barrier against environmental damage and attack by natural predators. In particular, this multilayer porous structure can be exceptionally tough to enhance the chance of survival for pupas while supporting their metabolic activity. Here, a fractional derivative is defined through the variational iteration method, and its application to explaining the outstanding thermal protection of insulation clothings with cocoon-like porous structure is elucidated. The fractal hierarchic structure of insulation clothings makes human body mathematically adapted for extreme temperature environment.