Abstract
The present work investigates the applicability and effectiveness of generalized proportional fractional integral ($\mathcal{GPFI}$
GPFI
) operator in another sense. We aim to derive novel weighted generalizations involving a family of positive functions n ($n\in \mathbb{N}$
n
∈
N
) for this recently proposed operator. As applications of this operator, we can generate notable outcomes for Riemann–Liouville ($\mathcal{RL}$
RL
) fractional, generalized $\mathcal{RL}$
RL
-fractional operator, conformable fractional operator, Katugampola fractional integral operator, and Hadamard fractional integral operator by changing the domain. The proposed strategy is vivid, explicit, and it can be used to derive new solutions for various fractional differential equations applied in mathematical physics. Certain remarkable consequences of the main theorems are also figured.
Weighted estimates of higher order commutators generated by BMO-functions and the fractional integral operator on Morrey spaces
