On boundedness of fractional integral operators via several kinds of convex functions

Yonghong Liu; Ghulam Farid; Dina Abuzaid; Hafsa Yasmeen; Yonghong Liu; Ghulam Farid; Dina Abuzaid; Hafsa Yasmeen

doi:10.3934/math.20221052

AIMS Mathematics

2022, Volume 7, Issue 10: 19167-19179. doi: 10.3934/math.20221052

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On boundedness of fractional integral operators via several kinds of convex functions

1.
School of Computer Science, Chengdu University, Chengdu, China
2.
Department of Mathematics, COMSATS University Islamabad, Attock Campus, Pakistan
3.
Department of Mathematics, King Abdul Aziz University, Saudi Arabia

Received: 26 June 2022 Revised: 17 August 2022 Accepted: 23 August 2022 Published: 30 August 2022
MSC : 26A33, 26D10, 31A10

For generalizations of concepts of different fields fractional derivative operators as well as fractional integral operators are useful notions. Our aim in this paper is to discuss boundedness of the integral operators which contain Mittag-Leffler function in their kernels. The results are obtained for strongly $ (\alpha, h-m) $-convex functions which hold for different kinds of convex functions at the same time. They also give improvements/refinements of many already published results.
- strongly $ (\alpha, h-m) $-convex function,
- generalized fractional integral operators,
- unified Mittag-Leffler function,
- bounds
Citation: Yonghong Liu, Ghulam Farid, Dina Abuzaid, Hafsa Yasmeen. On boundedness of fractional integral operators via several kinds of convex functions[J]. AIMS Mathematics, 2022, 7(10): 19167-19179. doi: 10.3934/math.20221052

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Abstract

For generalizations of concepts of different fields fractional derivative operators as well as fractional integral operators are useful notions. Our aim in this paper is to discuss boundedness of the integral operators which contain Mittag-Leffler function in their kernels. The results are obtained for strongly $ (\alpha, h-m) $-convex functions which hold for different kinds of convex functions at the same time. They also give improvements/refinements of many already published results.

References

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