Estimates related to Caputo derivatives using generalized modified $ h $-convex functions

Halim Benali; Mohammed Said Souid; Hatıra Günerhan; Unai Fernandez-Gamiz; Halim Benali; Mohammed Said Souid; Hatıra Günerhan; Unai Fernandez-Gamiz

doi:10.3934/math.20241398

AIMS Mathematics

2024, Volume 9, Issue 10: 28813-28827. doi: 10.3934/math.20241398

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Estimates related to Caputo derivatives using generalized modified $ h $-convex functions

1.
Laboratory of Informatic and Mathematics, Faculty of Mathematics and Informatic, University of Tiaret, Algeria
2.
Department of Economic Sciences, University of Tiaret, Tiaret, Algeria
3.
Department of Mathematics, Faculty of Education, Kafkas University, Kars, Turkey
4.
MEU Research Unit, Middle East University, Amman, Jordan
5.
Nuclear Engineering and Fluid Mechanics Department, University of the Basque Country UPV/EHU, Nieves Cano 12, 01006, Vitoria-Gasteiz, Spain

Received: 05 June 2024 Revised: 15 August 2024 Accepted: 20 August 2024 Published: 12 October 2024
MSC : 26A51, 26A33

In the present work, we have established some new fractional integral inequalities for functions whose $ k $th-derivatives are generalized modified $ h $-convex and symmetric about the midpoint involving the Caputo fractional derivatives. Many particular cases are obtained by using the findings.
- modified $ h $-convexity,
- convexity,
- Caputo fractional derivatives
Citation: Halim Benali, Mohammed Said Souid, Hatıra Günerhan, Unai Fernandez-Gamiz. Estimates related to Caputo derivatives using generalized modified $ h $-convex functions[J]. AIMS Mathematics, 2024, 9(10): 28813-28827. doi: 10.3934/math.20241398

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Abstract

In the present work, we have established some new fractional integral inequalities for functions whose $ k $th-derivatives are generalized modified $ h $-convex and symmetric about the midpoint involving the Caputo fractional derivatives. Many particular cases are obtained by using the findings.

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