The phenomena of senescence are widely observed during the process of cell mitosis at the cellular level. From the perspective of statistical mechanics, the senescence can be formulated by a random walk process whose dynamic and transitional properties decay as the number of transitions increases. To explore the impact of the senescence effects on anomalous diffusion, we propose a new subordinator by adding a senescence term $f\left(s\right)$ to the classical $\alpha$-stable subordinator and then establish the subordinated Langevin equation to characterize the subdiffusion with senescence effects. By taking the senescence term $f\left(s\right)$ in the specific form of power law, we evaluate the ensemble average and time average of the mean-squared displacements and derive the Fokker-Planck equations of the propagators. The quantitative analyses reveal different diffusion regimes for the scenarios of weak senescence and strong senescence. The results show that the strong senescence effect has a damping influence and slows down the subdiffusion, while the weak senescence effect has no impact on the subdiffusion at large-time limit. The proposed Langevin equation and the quantitative analyses provide a new perspective for studying the senescence effects in anomalous diffusion phenomena.

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• Anomalous diffusion
• Ergodic theory
• Fokker–Planck equation
• Langevin equation