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Estimations of Bounds on the Multiplicative Fractional Integral Inequalities Having Exponential Kernels

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Abstract

To investigate the fractional Hermite–Hadamard-type inequalities, a class of the multiplicative fractional integrals having exponential kernels is introduced. Some estimations of upper bounds for the newly introduced class of integral operators are obtained in terms of the established \(^*\)differentiable identity. And our results presented in this study are substantial generalizations of previous findings given by Ali et al. (Asian Res J Math 12:1–11, 2019). Three examples are also provided to identify the correctness of the results that occur with the change of the parameter \(\alpha \).

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Acknowledgements

The authors would like to thank the reviewer for his/her valuable comments and suggestions.

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Authors and Affiliations

  1. Department of Mathematics, College of Science, China Three Gorges University, Yichang, 443002, People’s Republic of China

    Yu Peng, Hao Fu & Tingsong Du

  2. Three Gorges Mathematical Research Center, China Three Gorges University, Yichang, 443002, People’s Republic of China

    Tingsong Du

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Correspondence to Tingsong Du.

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Peng, Y., Fu, H. & Du, T. Estimations of Bounds on the Multiplicative Fractional Integral Inequalities Having Exponential Kernels. Commun. Math. Stat. 12, 187–211 (2024). https://doi.org/10.1007/s40304-022-00285-8

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