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.

Grady et al. (Reports, 13 June 2014, p. 1268) studied dinosaur metabolism by comparison of maximum somatic growth rate allometry with groups of known metabolism. They concluded that dinosaurs exhibited mesothermy, a metabolic rate intermediate between endothermy and ectothermy. Multiple statistical and methodological issues call into question the evidence for dinosaur mesothermy.

3.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 3.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 3.3 The Allometry of Characteristic Response Time in Consumer-Resource Systems . . . . . . 46 3.4 Parametric and Demographic Perturbations . . . . . . . . . . . . . . . . . . . . . . . ...