From Leibniz'S Notation For Derivative To The Fractal Derivative, Fractional Derivative And Application In Mongolian Yurt

The fractal derivative is a natural extension of Leibniz's derivative for discontinuous fractal media. In this chapter three definitions are discussed, one of which is newly introduced and geometrically motivated. The fractal differential equations can be transferred into ordinary differential equations.Some fractional derivatives are derived from variational iteration algorithms, such as the well-known Riemann-Liouville fractional derivative, Jumarie's modification, and a new one.A yurt is a portable tent-like dwelling structure favored by Mongolian nomads for more than three millennia, it can be used even in harsh environments as low as negative 50 degrees centigrade. We conclude that the multi-layer structure of the felt cover, which mimics the design of a cocoon, is the key for weather proofing. A local fractional differential model is established to find an optimal thickness of the fractal hierarchy of the felt cover. A better understanding of the yurt mechanism could help the further design of yurt-like space suits and other protective clothes for special applications.