Model of the solar dynamo hardly reproduce the observations of the solar magnetic field. In the presence of strong magnetic field in a turbulent fully ionized medium, such as the solar interior, temporal and spacial re-correlations can occur. In the frame of mean-field MHD, these can be treated as spacial and temporal non-localities (memory effect). We found that the magnetic buoyancy occurring in the convective solar interior implies a non-linear temporal non-locality. This additional non-linearity leads to solutions that recover the morphological evolution of the solar magnetic field.