LAUSR

Dynamics in fractional order systems has been discussed extensively for presenting a possible guidance in the field of applied mathematics and interdisciplinary science. Within hundreds and thousands of reviews, regular papers and drafts, many fractional differential equations are presented for enjoying mathematical proof without clarifying the scientific background and physical principles. It seems that all nonlinear problems on integer order systems even networks can be confirmed as fractional order systems. This mini-review gives an appropriate clarification on fractional dynamical systems from the physical viewpoint, thereby presenting sufficient evidences for further study on fractional calculus. We argued that non-uniform diffusion, boundary effect and elastic deformation account for the calculation and estimation with fractional order on some physical variables, which can be mapped into dimensionless variables in the dynamical systems. In addition, some similar definitions for energy, wave propagation and diffusion are suggested to find reliable confirmation in the application of fractional calculus.