In this work, we introduce a new form of the quaternionic fractional uncertainty relation within the framework of quaternionic quantum mechanics. This is closely associated with the Li–Ostoja–Starzewski fractional gradient operator characterized by an order range of 0 < β ≤ 1 $$ 0<\beta \le 1 $$ . We explore a novel quaternionic Schrödinger equation and its specific implications particularly addressing solutions that lead to the emergence of position-dependent mass.
