Certain new weighted estimates proposing generalized proportional fractional operator in another sense

Abstract

Abstract The present work investigates the applicability and effectiveness of generalized proportional fractional integral ( GPFI $\mathcal{GPFI}$ ) operator in another sense. We aim to derive novel weighted generalizations involving a family of positive functions n ( n ∈ N $n\in \mathbb{N}$ ) for this recently proposed operator. As applications of this operator, we can generate notable outcomes for Riemann–Liouville ( RL $\mathcal{RL}$ ) fractional, generalized RL $\mathcal{RL}$ -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.

Keywords

• Integral inequality
• Generalized proportional fractional integral with respect to another function
• Increasing and decreasing functions