Fractional integral inequalities for $ h $-convex functions via Caputo-Fabrizio operator

Lanxin Chen; Junxian Zhang; Muhammad Shoaib Saleem; Imran Ahmed; Shumaila Waheed; Lishuang Pan; Lanxin Chen; Junxian Zhang; Muhammad Shoaib Saleem; Imran Ahmed; Shumaila Waheed; Lishuang Pan

doi:10.3934/math.2021374

AIMS Mathematics

2021, Volume 6, Issue 6: 6377-6389. doi: 10.3934/math.2021374

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Research article

Fractional integral inequalities for $ h $-convex functions via Caputo-Fabrizio operator

1.
Science College, Shijiazhuang University, 050035, China
2.
Department of Mathematics, University of Okara, Okara, Pakistan
3.
Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore Pakistan

Received: 19 December 2020 Accepted: 25 March 2021 Published: 12 April 2021
MSC : 26A51, 26A33, 26D15

The aim of this paper is to study $ h $ convex functions and present some inequalities of Caputo-Fabrizio fractional operator. Precisely speaking, we presented Hermite-Hadamard type inequality via $ h $ convex function involving Caputo-Fabrizio fractional operator. We also presented some new inequalities for the class of $ h $ convex functions. Moreover, we also presented some applications of our results in special means which play a significant role in applied and pure mathematics, especially the accuracy of a results can be confirmed by through special means.
- Capoto-Fabrizio fractional operator,
- $ h $-convexity,
- Hermite-Hadamard type inequality
Citation: Lanxin Chen, Junxian Zhang, Muhammad Shoaib Saleem, Imran Ahmed, Shumaila Waheed, Lishuang Pan. Fractional integral inequalities for $ h $-convex functions via Caputo-Fabrizio operator[J]. AIMS Mathematics, 2021, 6(6): 6377-6389. doi: 10.3934/math.2021374

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Abstract

The aim of this paper is to study $ h $ convex functions and present some inequalities of Caputo-Fabrizio fractional operator. Precisely speaking, we presented Hermite-Hadamard type inequality via $ h $ convex function involving Caputo-Fabrizio fractional operator. We also presented some new inequalities for the class of $ h $ convex functions. Moreover, we also presented some applications of our results in special means which play a significant role in applied and pure mathematics, especially the accuracy of a results can be confirmed by through special means.

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