Exploration of Some Novel Integral Inequalities Pertaining to the New Class of (k, ρ)-Conformable Fractional Integrals (Contemporary Mathematics, 2025)
Conformable integrals and derivatives have received more attention in recent years as a means of determining different kinds of inequalities. In the research work, we define a novel class of (k, ρ)-conformable fractional integrals ((k, ρ)-CFI). Also, we establish the refinement of the reverse Minkowski inequality incorporating the (k, ρ)-conformable fractional integral operators. The proposed (k, ρ)-conformable fractional integral operators are used to present the two new theorems that correlate with this inequality, along with declarations and verifications of other inequalities. The inequalities presented in this work are more general as compared to the existing literature. The special cases of our main findings are given in the paper.
Keywords: conformable fractional derivative; conformable fractional integral; inequalities; fractional integrals