Sayyiduna Abdullah bin Abbas (may Allah be pleased with them both) says: A man came to the Prophet (peace and blessings be upon him) and said: My mother is of advanced age; we cannot seat her on a mount, she is unable to stay mounted, and if we tie her (to the mount), we fear she will die. Shall I perform Hajj on her behalf? He (peace and blessings be upon him) said: "Yes."
The narrations of Ibn Sirin from Ibn Abbas are mursal (with a broken chain). It has also been narrated from Awf bin Abi Jamilah, from Ibn Sirin, from Abu Hurayrah, but the narration of Ayyub is more authentic. And Allah knows best.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الحج / 8636