Is he Obliged to Offer an Oath Expiation since only Part of it was Fulfilled?

Answer:

All perfect praise be to Allah, The Lord of the Worlds, and may His peace and blessings be upon our Prophet Muhammad and upon all of his family and companions. If the matters that you vowed to do were acts of devotion then you are liable and obliged to fulfill them. However, if they weren't acts of devotion then you aren't obliged to fulfill them nor to offer an expiation according to our Madhab(Shafii school of thought). Yet, paying an expiation in this case would be better in order to avoid disagreement among Muslim scholars and to be on the safe side. Al-Imam Al-Shirbini (May Allah have mercy on his soul) said (what means):" If a person vowed to fulfill a permissible act such as sleeping, eating…..etc or to quit eating dessert and the like then he isn't obliged to fulfill such matters since, Abu Dawood(May Allah be pleased with him) reported that the Prophet (PBUH) said(what means):" No vow is to be fulfilled save for the sake of Allah.". In addition, Ibn 'Abbas (May Allah be pleased with them) reported: While the Prophet (PBUH) was delivering Khutbah (religious talk), he noticed a man who was standing, so he asked about him and was told that he was Abu Israel who had taken a vow to remain standing and not sit, or go into the shade, or speak while observing fasting. Thereupon Messenger of Allah (PBUH) said, "Tell him to speak, to go into the shade, to sit and to complete his fast". [Mughni Al-Muhtaj 6/235-236]. And Allah knows best.