Trapping reactions with subdiffusive traps and particles characterized by different anomalous diffusion exponents

A number of results for reactions involving subdiffusive species, all with the same anomalous exponent $\gamma$, have recently appeared in the literature and can often be understood in terms of a subordination principle whereby time $t$ in ordinary diffusion is replaced by $t^{\gamma }$. However, very few results are known for reactions involving different species characterized by different anomalous diffusion exponents. Here we study the reaction dynamics of a (sub)diffusive particle surrounded by a sea of (sub)diffusive traps in one dimension. We find rigorous results for the asymptotic survival probability of the particle in most cases, with the exception of the case of a particle that diffuses normally while the anomalous diffusion exponent of the traps is smaller than $2∕3$.