A new fractional operator of variable order: application in the   description of anomalous diffusion
  In this paper, a new fractional operator of variable order with the use of the monotonic increasing function is proposed in sense of Caputo type. The properties in term of the Laplace and Fourier transforms are analyzed and the results for the anomalous diffusion equations of variable order are discussed. The new formulation is efficient in modeling a class of concentrations in the complex transport process. 
Xiao-Jun Yang (School of Mechanics and Civil Engineering, China   University of Mining and Technology, State Key Laboratory ...
cond-mat.stat-mech