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 ≤1. We explore a novel Quaternionic Schrödinger equation and its specific implications, particularly addressing solutions that lead to the emergence of position-dependent mass. Additionally, we validate the theory by comparing it against the observed maximum wavelengths in the 1,3,5-hexatriene molecule.