On some Hermite-Hadamard inequalities involving \(k\)-fractional operators. (English) Zbl 1504.26071
Summary: The main objective of this paper is to establish some new Hermite-Hadamard type inequalities involving \(k\)-Riemann-Liouville fractional integrals. Using the convexity of differentiable functions some related inequalities have been proved, which have deep connection with some known results. At the end, some applications of the obtained results in error estimations of quadrature formulas are also considered.
MSC:
| 26D15 | Inequalities for sums, series and integrals |
| 26A33 | Fractional derivatives and integrals |
| 33B15 | Gamma, beta and polygamma functions |
| 26A51 | Convexity of real functions in one variable, generalizations |
References:
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