  Anomalous (or non-Fickian) diffusion has been widely found in fluid reactive
transport and the traditional advection diffusion reaction equation based on
Fickian diffusion is proved to be inadequate to predict this anomalous
transport of the reactive particle in flows. To capture the complex couple
effect among advection, diffusion and reaction, and the energy-dependent
characteristics of fluid reactive anomalous transport, in the present paper we
analyze $A\rightarrow B$ reaction under anomalous diffusion with waiting time
depending on the preceding jump length in linear flows, and derive the
corresponding master equations in Fourier-Laplace space for the distribution of
A and B particles in continuous time random walks scheme. As examples, the
generalized advection diffusion reaction equations for the jump length of
Gaussian distribution and l\'evy flight with the probability density function
of waiting time being quadratic dependent on the preceding jump length are
obtained by applying the derived master equations.
