Reference: Fataawa Ramadhaan – Volume 2, Page 703, Fatwa No.710
al-Muntaqaa min Fataawa Shaykh Saalih Ibn Fowzaan – Volume 3, Page 151
Question: Regarding al-ayyaam al-beedh (13th, 14th and 15th of the lunar month), is it true that the Messenger fasted them when he was travelling as well as when he was back home, or is it something recommended only?
Response: The Messenger ﷺ used to exert himself in offering voluntary fasts, and he would fast [so much] that it would be said he does not stop fasting, and (likewise) he would not fast until it would be said he does not fast; So the Messenger ﷺ would exert himself in offering voluntary fasts both whilst travelling as well as when he was back home.
As for him offering the voluntary fasts during al-ayyaam al-beedh (13th, 14th and 15th of the lunar month), then I do not know as nothing currently comes to my mind about this.