  We present a \textit{mesoscopic}description of the anomalous transport and
reactions of particles in spiny dendrites. As a starting point we use two-state
Markovian model with the transition probabilities depending on residence time
variable. The main assumption is that the longer a particle survives inside
spine, the smaller becomes the transition probability from spine to dendrite.
We extend a linear model presented in [PRL, \textbf{101}, 218102 (2008)] and
derive the nonlinear Master equations for the average densities of particles
inside spines and parent dendrite by eliminating residence time variable. We
show that the flux of particles between spines and parent dendrite is not local
in time and space. In particular the average flux of particles from a
population of spines through spines necks into parent dendrite depends on
chemical reactions in spines. This memory effect means that one can not
separate the exchange flux of particles and the chemical reactions inside
spines. This phenomenon does not exist in the Markovian case. The flux of
particles from dendrite to spines is found to depend on the transport process
inside dendrite. We show that if the particles inside a dendrite have constant
velocity, the mean particle's position $<x(t)> $ increases as $t^{\mu}$ with
$\mu <1$ (anomalous convection). We derive a fractional convection-diffusion
equation for the total density of particles.
