The　difficulty　in　solving　distributed　order　differential　equations　lies　in　the　fact　that　the　order　of　the　derivative　is　distributed　within　a　finite　interval.　Considering　the　time　derivative　Caputo　type　and　spatial　derivative　Riesz　type　distributed　diffusion　equation,　we　obtain　its　series　solution　by　spectral　methods　and　prove　its　convergence,　moreover,　a　specific　accuracy　estimate　of　its　numerical　format　is　given.　©　(2025),　(International　Association　of　Engineers).　All　Rights　Reserved.