Weighted Ostrowski, trapezoid and midpoint type inequalities for RiemannLiouville fractional integrals

Hüseyin Budak; Ebru Pehlivan; Hüseyin Budak; Ebru Pehlivan

doi:10.3934/math.2020131

AIMS Mathematics

2020, Volume 5, Issue 3: 1960-1984. doi: 10.3934/math.2020131

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Research article

Weighted Ostrowski, trapezoid and midpoint type inequalities for RiemannLiouville fractional integrals

Hüseyin Budak ^,,
Ebru Pehlivan

Department of Mathematics, Faculty of Science and Arts, Düzce University, Düzce, Turkey

Received: 07 October 2019 Accepted: 13 February 2020 Published: 20 February 2020
MSC : 26B25, 26D10, 26D15

Our first aim is to establish two new identities for differentiable function involving Riemann-Liouville fractional integrals. Then, we obtain some new weighted versions of fractional trapezoid and Ostrowski type inequalities. Moreover, we give some weighted fractional midpoint type inequalities as special cases.
- trapezoid inequality,
- Ostrowski inequality,
- fractional integral operators,
- convex function,
- concave function
Citation: Hüseyin Budak, Ebru Pehlivan. Weighted Ostrowski, trapezoid and midpoint type inequalities for RiemannLiouville fractional integrals[J]. AIMS Mathematics, 2020, 5(3): 1960-1984. doi: 10.3934/math.2020131

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Abstract

Our first aim is to establish two new identities for differentiable function involving Riemann-Liouville fractional integrals. Then, we obtain some new weighted versions of fractional trapezoid and Ostrowski type inequalities. Moreover, we give some weighted fractional midpoint type inequalities as special cases.

References

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