ANSWER:

This is permissible. 

Can a woman fast on 9th and 10th of Muharram with niyyah of missed Ramadan fasts and Muharram fasts?

Fasting | August 6, 2022 2:23 pm
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Is there any reference that Prophet Muhammad salallahu walahi wa sallam fasted on his birthday?
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Can we fast on 10th muharram only without fasting on 9th or 11th as I just recovered from jaundice few days back?