Hadith.2822 - In a narration by Muawiyah ibn Ammar from Imam Abu Abdullah عليه السلام:
"The injured person (who cannot walk) should be carried to throw the pebbles at the Jamara, while for the person afflicted with severe illness (such as diarrhea), the stoning can be done on their behalf, and prayers can also be performed on their behalf."
Muawiyah also narrates leniency from the Imam, allowing both circumambulation and stoning to be performed on behalf of such individuals.