Progress in Fractional Differentiation & Applications

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Recently, many researchers have published work on the Hermite-Hadamard inequalities, due to their immense importance in the fields of numerical analysis, statistics, optimization and convexity theory. . In this paper, certain new Hermite-Hadamard type integral inequalities have been established using the (k − r) Riemann-Liouville fractional integral operator. We present various inequalities based on different types of the convex functions such as quasi-convex, l-convex, η-convex in the second sense and (β,l)-convex functions. Also, we derive Hermite-Hadamard type inequalities for the product of two l-convex functions and two (β,l)-convex functions using (k − r) Riemann-Liouville fractional integral operator. The results obtained in our work will be helpful in the further study of the convex functions and in the evaluation of the certain mathematical problems.

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