Search

Integral inequalities with generalized convexity play an important role in both applied and theoretical mathematics. The theory of integral inequalities is currently one of the most rapidly developing areas of mathematics due to its wide range of applications. In this paper, we study the concept of higher-order strongly exponentially convex functions and establish a new Hermite–Hadamard inequality for the class of strongly exponentially convex functions of higher order. Further, we derive some new integral inequalities for Riemann–Liouville fractional integrals via higher-order strongly exponentially convex functions. These findings include several well-known results and newly obtained results as special cases. We believe that the results presented in this paper are novel and will be beneficial in encouraging future research in this field. [ABSTRACT FROM AUTHOR]

In mathematics and the applied sciences, as a very useful tool, fractional calculus is a basic concept. Furthermore, in many areas of mathematics, it is better to use a new hybrid fractional operator, which combines the proportional and Caputo operators. So we concentrate on the proportional Caputo-hybrid operator because of its numerous applications. In this research, we introduce a novel extension of the Hermite–Hadamard-type inequalities for proportional Caputo-hybrid operator and establish an identity. Then, taking into account this novel generalized identity, we develop some integral inequalities associated with the left-side of Hermite–Hadamard-type inequalities for proportional Caputo-hybrid operator. Moreover, to illustrate the newly established inequalities, we give some examples with the help of graphs. [ABSTRACT FROM AUTHOR]