A New Approach of Milne-type Inequalities Based on Proportional Caputo-Hybrid Operator

Abstract

In this study, we first offer a novel integral identity using twice-differentiable convex mappings for the proportional Caputo-hybrid operator. Next, we demonstrate many integral inequalities related to the Milne-type integral inequalities for proportional Caputo-hybrid operator with the use of this newly discovered identity. Also, we present several examples along with their corresponding graphs in order to provide a better understanding of the newly obtained inequalities. Finally, we observe that the obtained results improve and generalize some of the previous results in the area of integral inequalities. 2010 Mathematics Subject Classification. 26D07, 26D10, 26A33