Abstract
We investigate a diffusion process by considering simultaneously stochastic resetting and linear reaction kinetics in the continuous time random walk approach. We first consider the formalism for a single species and then extend it to multiple species. We perform the analysis by considering a general probability density function for the random walk, allowing us to obtain various behaviors for the waiting time and jumping probability distributions. The behavior of these distributions has implications for the diffusion-like equations which emerge from this approach and can be connected to different fractional operators with singular or nonsingular kernels. We also show that diffusion-like equations can exhibit a large class of behaviors related to different processes, particularly anomalous diffusion.
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