Solution of a nonlocal boundary value problem of diffusion-convective transfer of radioactive substances in the lithosphere-atmosphere system

The article studies a boundary value problem for describing non-local and nonstationary diffusion-convective transfer of radioactive material in the lithosphere-atmosphere system. The non-locality of the transfer is due to heredity effects in the upper layer of the lithosphere and is described from a mathematical point of view using fractional Gerasimov-Caputo derivatives with respect to time and fractional Riemann-Liouville derivatives with respect to the spatial coordinate. Boundary conditions are specified both at the outer boundaries and at the inner lithosphere-atmosphere boundary. The solution to the problem is found using the integral Laplace transform and is given in terms of the generalized Wright function.