A Fractional Model for the Allometric Scaling Laws

Abstract

From the available literature, the allometric scaling laws generally exist in biology, ecology, etc. These scaling laws obey power law distributions. A possibly better approach to characterize the power law is to utilize fractional derivatives. In this paper, we establish a fractional differential equation model for this allometry by using the Caputo fractional derivatives.

Numerical Detection of the Lowest “Efficient Dimensions” for Chaotic Fractional Differential Systems

“…To model and/or analyze fractional differential equation [26], etc, especially to disclose the dynamics of fractional differential systems, have been become more and more important due to their real-world applications [4,7]. For chaotic fractional differential systems, the definition of efficient dimension was firstly mentioned in [13], where a novel but not mathematically rigorous numerical method was applied to the fractional Lorenz system, and where to seek the smallest efficient dimension for the chaotic fractional system was also proposed.…”