Fractional Newton-type inequalities for twice differentiable functions via proportional Caputo-Hybrid operator

Abstract

In this paper, we first propose a novel integral identity for twice-differentiable convex mappings using the proportional Caputo-hybrid operator. Then, with the assistance of this identity, we derive various integral inequalities for the proportional Caputo-hybrid operator, which are connected to the Newton-type integral inequalities. Also, we establish a number of Newton-type inequalities for mappings of bounded variation. Finally, we note that the given results improve and generalize some of the previous findings on the subject of integral inequality. Our findings represent the pioneering work in this direction.