  By considering the master equation of the totally asymmetric exclusion
process on a one-dimensional lattice and using two types of boundary conditions
(i.e. interactions), two new families of the multi-species reaction-diffusion
processes, with particle-dependent hopping rates, are investigated. In these
models (i.e. reaction-diffusion and drop-push systems), we have the case of
distinct particles where each particle $A_\alpha$ has its own intrinsic hopping
rate $v_{\alpha}$. They also contain the parameters that control the
annihilation-diffusion rates (including pair-annihilation and coagulation to
the right and left). We obtain two distinct new models. It is shown that these
models are exactly solvable in the sense of the Bethe anstaz. The two-particle
conditional probabilities and the large-time behavior of such systems are also
calculated.
