Abdul Muktadir is another spelling of Abdul Muqtadir, which is a good name that means “servant of the Able One”, which means “servant of Allah”. Abdul is short for Abd al, therefore writing Abdul al Muktadir is like writing Abd al al Muktadir, which is incorrect. The correct name should be Abdul Muktadir or Abd al Muktadir.
Writing Abdul al Muqtadir means “servant of the the Able One”, you can see the double “the the”. It is a grammatical error. It doesn’t change the meaning, it is just not correct. But you can keep it that way if you like, as it is not forbidden, and many names do not follow grammar rules.