Integral inequalities for a fractional operator of a function with respect to another function with nonsingular kernel. (English) Zbl 1485.26020
Summary: At first, we construct a connection between the Atangana-Baleanu and the Riemann-Liouville fractional integrals of a function with respect to a monotone function with nonsingular kernel. By examining this relationship and the iterated form of Prabhakar fractional model, we are able to find some new Hermite-Hadamard inequalities and related results on integral inequalities for the two models of fractional calculus which are defined using monotone functions with nonsingular kernels.
MSC:
| 26D07 | Inequalities involving other types of functions |
| 26D10 | Inequalities involving derivatives and differential and integral operators |
| 26D15 | Inequalities for sums, series and integrals |
| 26A33 | Fractional derivatives and integrals |
| 33E12 | Mittag-Leffler functions and generalizations |
Software:
MLReferences:
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