Some Hermite–Hadamard-Type Fractional Integral Inequalities Involving Twice-Differentiable Mappings

Abstract

The theory of fractional analysis has been a focal point of fascination for scientists in mathematical science, given its essential definitions, properties, and applications in handling real-life problems. In the last few decades, many mathematicians have shown their considerable interest in the theory of fractional calculus and convexity due to their wide range of applications in almost all branches of applied sciences, especially in numerical analysis, physics, and engineering. The objective of this article is to establish Hermite-Hadamard type integral inequalities by employing the k-Riemann-Liouville fractional operator and its refinements, whose absolute values are twice-differentiable h-convex functions. Moreover, we also present some special cases of our presented results for different types of convexities. Moreover, we also study how q-digamma functions can be applied to address the newly investigated results. Mathematical integral inequalities of this class and the arrangements associated have applications in diverse domains in which symmetry presents a salient role.

Fractional Calculus for Convex Functions in Interval-Valued Settings and Inequalities

“…In the future, we will use generalized interval and fuzzy Riemann-Liouville fractional operators to investigate this concept for generalized left and right convex I•V-Fs and F-I•V-Fs by using interval Katugampola fractional integrals and fuzzy Katugampola fractional integrals. For applications, see [53][54][55][56].…”

Improvements of Slater’s Inequality by Means of 4-Convexity and Its Applications

“…It has been ascertained that, the convex functions played a very meaningful performance in the field of mathematical inequalities [2,[21][22][23][24]. There are many consequential inequalities that have been established via convex functions, such as majorization [25], Favard's [26], Hermaite-Hadamard inequalities [27] and many more [28][29][30][31][32]. Besides these inequalities, one of the most attractive inequalities for the class of convex functions is the Jensen inequality [10].…”

New Developments of Hermite–Hadamard Type Inequalities via s-Convexity and Fractional Integrals

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