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This paper pays attention to develop a variable-order fractal derivative   model for anomalous diffusion. Previous investigations have indicated that   the medium structure, fractal dimension or porosity may change with time or   space during solute transport processes, results in time or spatial dependent   anomalous diffusion phenomena. Hereby, this study makes an attempt to   introduce a variable-order fractal derivative diffusion model, in which the   index of fractal derivative depends on temporal moment or spatial position,   to characterize the above mentioned anomalous diffusion (or transport)   processes. Compared with other models, the main advantages in description and   the physical explanation of new model are explored by numerical simulation.   Further discussions on the dissimilitude such as computational efficiency,   diffusion behavior and heavy tail phenomena of the new model and   variable-order fractional derivative model are also offered

A variable-order fractal derivative model for anomalous diffusion