MMN-4903
A novel method for Milne-type inequalities using proportional Caputo-hybrid operator
İzzetti̇n Demi̇r;Abstract
In mathematics and the applied sciences, fractional calculus is a significant generalization and a very useful tool as it overcomes many limitations of classical analysis. More importantly, it is better to use the new hybrid fractional operator, which merges the proportional and Caputo operators, in many computer science and mathematics domains. In this study, because of its numerous applications, we concentrate on the proportional Caputo-hybrid operator. Firstly, we propose a new integral identity with the help of twice-differentiable convex mappings for the proportional Caputo-hybrid operator. Then, with the help of this newly found identity, we establish several integral inequalities related to the Milne-type integral inequalities for proportional Caputo-hybrid operator. Also, we obtain
various Milne-type inequalities for bounded mappings and mappings of bounded
variation. Finally, we point out that the obtained results enhance and
generalize some of the previous findings in the field of integral inequalities. These results are the first kind of such results in this direction.
Vol. 26 (2025), No. 2, pp. 701-725