Thispaperfocusesonnonlocalintegralboundaryvalueproblemsforellipticdifferential-operatorequations.HeregivenconditionsguaranteethatmaximalregularityandFredholmnessinL_pspaces.TheseresultsareappliedtotheCauchyproblemforabstractparabolicequations,itsinfinitesystemsandboundaryvalueproblemsforanisotropicpartialdifferentialequationsinmixedL_pnorm.