### AIMS Mathematics

2021, Issue 2: 1889-1904. doi: 10.3934/math.2021115
Research article Special Issues

# Fractional inequalities of the Hermite–Hadamard type for $m$-polynomial convex and harmonically convex functions

• Received: 21 October 2020 Accepted: 27 November 2020 Published: 03 December 2020
• MSC : 26D15, 26A51, 26D10

• In this paper, it is our purpose to establish some new fractional inequalities of the Hermite–Hadamard type for the $m$-polynomial convex and harmonically convex functions. Our results involve the Caputo–Fabrizio and $\zeta$-Riemann–Liouville fractional integral operators. They generalize, complement and extend existing results in the literature. By taking $m\geq 2$, we deduce loads of new and interesting inequalities. We expect that the thought laid out in this work will provoke advance examinations in this course.

Citation: Eze R. Nwaeze, Muhammad Adil Khan, Ali Ahmadian, Mohammad Nazir Ahmad, Ahmad Kamil Mahmood. Fractional inequalities of the Hermite–Hadamard type for $m$-polynomial convex and harmonically convex functions[J]. AIMS Mathematics, 2021, 6(2): 1889-1904. doi: 10.3934/math.2021115

### Related Papers:

• In this paper, it is our purpose to establish some new fractional inequalities of the Hermite–Hadamard type for the $m$-polynomial convex and harmonically convex functions. Our results involve the Caputo–Fabrizio and $\zeta$-Riemann–Liouville fractional integral operators. They generalize, complement and extend existing results in the literature. By taking $m\geq 2$, we deduce loads of new and interesting inequalities. We expect that the thought laid out in this work will provoke advance examinations in this course.

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