Journal
FRACTAL AND FRACTIONAL
Volume 6, Issue 3, Pages -Publisher
MDPI
DOI: 10.3390/fractalfract6030171
Keywords
Hermite-Hadamard inequality; Caputo-Fabrizio operator; Pachpatte type inequality; Holder's inequality; Holder-Ican inequality
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Funding
- Taif University, Taif, Saudi Arabia [TURSP 2020/155]
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In this article, a new approach is presented to derive generalized midpoint-type Hermite-Hadamard inequality and Pachpattetype inequality using a new fractional integral operator related to the Caputo-Fabrizio derivative. A new fractional identity for differentiable convex functions of first order is proved. Utilizing these results and various inequalities, new estimations of the Hermite-Hadamard H-H type inequality as refinements are obtained. Applications to special means and trapezoidal quadrature formula are introduced to verify the accuracy of the results.
In this article, a generalized midpoint-type Hermite-Hadamard inequality and Pachpattetype inequality via a new fractional integral operator associated with the Caputo-Fabrizio derivative are presented. Furthermore, a new fractional identity for differentiable convex functions of first order is proved. Then, taking this identity into account as an auxiliary result and with the assistance of Holder, power-mean, Young, and Jensen inequality, some new estimations of the Hermite-Hadamard H-H type inequality as refinements are presented. Applications to special means and trapezoidal quadrature formula are presented to verify the accuracy of the results. Finally, a brief conclusion and future scopes are discussed.
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