The left Riemann-Liouville fractional Hermite-Hadamard type inequalities for convex functions

Abstract

In this paper, with a new approach, a new fractional Hermite-Hadamard type inequalities for convex functions is obtained by using only the left Riemann-Liouville fractional integral. Also, to have new fractional trapezoid and midpoint type inequalities for the differentiable convex functions, two new equalities are proved. Our results generalize earlier studies. We expect that this study will be lead to the new fractional integration studies for Hermite-Hadamard type inequalities.

Some parameterized inequalities by means of fractional integrals with exponential kernels and their applications

“…As a result, some well-known integral inequalities by the approach of fractional calculus have been carried out by many authors, including Chen [4] and Mohammed [23] in the study of the Hermite-Hadamard inequality, and Set et al [29] in the Simpson type integral inequality for Riemann-Liouville fractional integrals, Chen and Katugampola [5] in the Hermite-Hadamard-Fejér type inequality for Katugampola fractional integrals, Wang et al [33] in the Ostrowski type inequality for Hadamard fractional integrals, Du et al [8] in the extensions of trapezium inequalities for k-fractional integrals, and Khan et al [14] in the Hermite-Hadamard inequality for conformable fractional integrals. For more results related to the fractional integral operators, the interested reader is directed to [1,11,13,16,17,21,25,28,30] and the references cited therein.…”

The Hermite–Hadamard–Jensen–Mercer Type Inequalities for Riemann–Liouville Fractional Integral

“…Most popular of them is the Riemann-Liouville fractional operator given in the following definition [19][20][21][22]. Definition 3 (see [23,24]). Let ψ be an integrable function defined on [m, M].…”

Certain parameterized inequalities arising from fractional integral operators with exponential kernels

“…In consequence, certain well-known integral inequalities through the method of fractional calculus have been carried out by many authors, including Chen [3] and Mohammed [24] in the research of the Hermite-Hadamard inequality, and Set et al [28] in the Simpson type integral inequality for Riemann-Liouville fractional integral operators, Wang et al [32] in the Ostrowski type inequality for Hadamard fractional integral operators, Chen and Katugampola [4] in the Fejér-Hermite-Hadamard type inequality for Katugampola fractional integral operators, Khan et al [15] in the Hermite-Hadamard inequality for conformable fractional integral operators, and Du et al [9] in the extensions of trapezium inequalities for k-fractional integral operators. With respect to more results in connection with the fractional integral operators, we refer the interested readers to [1,11,13,17,18,22,26,27,29] and the related references therein.…”