  Continuous time random walks have random waiting times between particle
jumps. We define the correlated continuous time random walks (CTRWs) that
converge to fractional Pearson diffusions (fPDs). The jumps in these CTRWs are
obtained from Markov chains through the Bernoulli urn-scheme model and
Wright-Fisher model. The jumps are correlated so that the limiting processes
are not L\'evy but diffusion processes with non-independent increments. The
waiting times are selected from the domain of attraction of a stable law
