Abstract
In this paper, the well-posedness of fractional random differential equations (FRDEs) involving Hilfer-Katugampola fractional derivative (HKFD) is discussed. The sufficient conditions to existence of solutions for FRDEs involving initial, nonlocal and impulsive conditions are generated using standard fixed point theorems. Further the stability of solution is verified by the concept proposed by Ulam. Uniqueness solutions of initial value problems for FRDEs using picards iterative techique and continuous dependence of data are also discussed.