Hermite–Hadamard Type Inequalities Involving k-Fractional Operator for (h¯,m)-Convex Functions

Abstract

The principal motivation of this paper is to establish a new integral equality related to k-Riemann Liouville fractional operator. Employing this equality, we present several new inequalities for twice differentiable convex functions that are associated with Hermite–Hadamard integral inequality. Additionally, some novel cases of the established results for different kinds of convex functions are derived. This fractional integral sums up Riemann–Liouville and Hermite–Hadamard’s inequality, which have a symmetric property. Scientific inequalities of this nature and, particularly, the methods included have applications in different fields in which symmetry plays a notable role. Finally, applications of q-digamma and q-polygamma special functions are presented.

Solution of a Fractional Integral Equation Using the Darbo Fixed Point Theorem

“…In [5], Sahoo et al developed numerous new inequalities for twice differentiable convex functions that are coupled with the Hermite-Hadamard integral inequality by using an integral equality related to the k-Riemann-Liouville fractional operator. In addition, for various types of convex functions, certain fresh examples of the established conclusions are derived.…”

Some Novel Fractional Integral Inequalities over a New Class of Generalized Convex Function

“…In the last few decades, many mathematicians and research scholars have concentrated their great contributions and attention on the study of this inequality. A few scientists have determined new variations related to convex functions; for instance, see [35][36][37][38][39] and the references cited therein. In addition, it is impressive that convexity offers multiple thoughts and fruitful applications in both pure and applied science.…”

Pólya–Szegö Integral Inequalities Using the Caputo–Fabrizio Approach

“…Recently, many researchers in several fields have found different results about some known fractional calculus and applications by means of the Riemann-Liouville [5][6][7][8][9][10][11], k-Riemann Liouville [12,13], Caputo [5,12,14], Hadamard [15,16], Marichev-Saigo-Maeda [17], Saigo [18][19][20], Katugamapola [21], Atangana-Baleanu [22] and some other fractional integral operators. Many mathematicians have worked on the Pólya-Szegö inequalities using various fractional integral operators in recent years (see [23][24][25][26]).…”