  Based on the theory of continuous time random walks (CTRW), we build the
models of characterizing the transitions among anomalous diffusions with
different diffusion exponents, often observed in natural world. In the CTRW
framework, we take the waiting time probability density function (PDF) as an
infinite series in three parameter Mittag-Leffler functions. According to the
models, the mean squared displacement of the process is analytically obtained
and numerically verified, in particular, the trend of its transition is shown;
furthermore the stochastic representation of the process is presented and the
positiveness of the PDF of the position of the particles is strictly proved.
Finally, the fractional moments of the model are calculated, and the analytical
solutions of the model with external harmonic potential are obtained and some
applications are proposed.
