A nonlocal diffusion model of a single species with age structure

Using theory of Fourier transformation, Dirac-δ function and von Foerster rule with nonlocal diffusion operator, we derive a single species population model with two age stages: juvenile and mature, which includes nonlocal dispersal both in diffusion and reaction. We found that the nonlocal reaction kernel function for mature population depends on the kernel function of diffusion for two age stages. This model takes the local diffusion model with only Laplacian operator or Laplacian operator combining with convection operator as particular examples. The existence, uniqueness, positivity and boundedness of initial value problem are also investigated in the present article. As a new model, its dynamics is worthy to be explored in the future work.