▁descent ▁to ▁Is m ā ‘ il ▁b . ▁Ja ʿ far ▁and ▁his ▁son ▁Muhammad ▁b . ▁Is m ā ʿ ī l , ▁the ▁first ▁F at im id ▁C ali ph ▁Abd ul lah ▁al - M ah di ▁B illa h ▁design ates ▁Ja ʿ far ' s ▁el dest ▁son ▁ ʿ Ab d ▁All ā h ▁as ▁his ▁for ef ather . ▁According ▁to ▁ ʿ Ab dal lah ▁al - M ah di ▁B illa h , ▁ ʿ Ab d ▁All ā h ▁ibn ▁Ja ' far ▁had ▁called ▁himself ▁Is m ā ʿ ī l ▁ibn ▁Ja ʿ far ▁for ▁the ▁sake ▁of ▁ta q iy ya , ▁and ▁each ▁of ▁his ▁success ors ▁had ▁assumed ▁the ▁name ▁Muhammad . ▁ ʿ Ab dal lah ▁al - M ah di ▁B illa h ▁explains ▁the ▁gene al ogy ▁of ▁the ▁F at im id ▁C ali ph s ▁and ▁he ▁claims ▁F at im id ▁ancest ry ▁by ▁declaring ▁himself ▁to ▁be ▁ ʿ A li ▁ibn ▁al - Ḥ us ay n ▁ibn ▁A ḥ mad ▁ibn ▁ ʿ Ab ad ull ā h ▁ibn ▁ ʿ Ab d ▁All ā h ▁ibn ▁Ja ʿ far ▁al - S adi q . ▁But ▁the ▁Im am ah ▁( Is mail i ▁doctrine ) ▁was ▁later ▁form ulated ▁in ▁a ▁different ▁manner ▁since ▁ ʿ Ab dal lah ▁al - M ah di ▁B illa h ' s ▁explanation ▁of ▁his ▁ancest ry ▁was