Generalized proportional fractional integral inequalities for convex functions

Majid K. Neamah; Alawiah Ibrahim; Majid K. Neamah; Alawiah Ibrahim

doi:10.3934/math.2021625

AIMS Mathematics

2021, Volume 6, Issue 10: 10765-10777. doi: 10.3934/math.2021625

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Research article

Generalized proportional fractional integral inequalities for convex functions

Majid K. Neamah ,
Alawiah Ibrahim ^,

Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, Malaysia

Received: 16 March 2021 Accepted: 19 July 2021 Published: 26 July 2021
MSC : 26A33, 26D10, 26D53

In this paper, we establish some inequalities for convex functions by applying the generalized proportional fractional integral. Some new results by using the linkage between the proportional fractional integral and the Riemann-Liouville fractional integral are obtained. Moreover, we give special cases of our reported results. Obtained results provide generalizations for some of the current results in the literature by applying some special values to the parameters.
- proportional fractional integral,
- fractional inequalities,
- convex function
Citation: Majid K. Neamah, Alawiah Ibrahim. Generalized proportional fractional integral inequalities for convex functions[J]. AIMS Mathematics, 2021, 6(10): 10765-10777. doi: 10.3934/math.2021625

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Abstract

In this paper, we establish some inequalities for convex functions by applying the generalized proportional fractional integral. Some new results by using the linkage between the proportional fractional integral and the Riemann-Liouville fractional integral are obtained. Moreover, we give special cases of our reported results. Obtained results provide generalizations for some of the current results in the literature by applying some special values to the parameters.

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