Is it obligatory to fulfill a vow to fast for a month or 40 days for the healing of a mother from chronic coughing that has fluctuated between recovery and recurrence?

A conditional vow is disliked, and it does not bring about anything Allah has not decreed. However, it must be fulfilled if the condition occurs, based on the Prophet's (peace be upon him) saying: "Whoever vows to obey Allah, let him obey Him." Fulfillment is not obligatory unless the condition is fully met. If the healing upon which the vow was conditioned occurs, then it must be fulfilled, unless you intended a healing after which the illness would not return. If you are uncertain about the duration of the vowed fasting, then you are obligated to fast the shortest duration of which you are certain.