10.1007/s40096-021-00445-x

On the fractional integral inclusions having exponential kernels for interval-valued convex functions

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  • Taichun Zhou1,
  • Zhengrong Yuan1,
  • Tingsong Du*2,
  1. Department of Mathematics, College of Science, China Three Gorges University, Yichang, CN
  2. Department of Mathematics, College of Science, China Three Gorges University, Yichang, CN Three Gorges Mathematical Research Center, China Three Gorges University, Yichang, CN

Published in Issue 2021-10-29

How to Cite

Zhou, T., Yuan, Z., & Du, T. (2021). On the fractional integral inclusions having exponential kernels for interval-valued convex functions. Mathematical Sciences, 17(2 (June 2023). https://doi.org/10.1007/s40096-021-00445-x
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Abstract

Abstract The purpose of the present paper is to establish certain fractional integral inclusions having exponential kernels, which are related to the Hermite–Hadamard, Hermite–Hadamard–Fejér, and Pachpatte type inequalities. These results allow us to obtain a new class of inclusions which can be viewed as some substantial generalizations of the previously reported results. Also, the graphical representations for the results are utilized to identify the correctness of the investigated inclusion relations that occur with the change of the parameter α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document} .

Keywords

  • Fractional integrals,
  • Interval-valued functions,
  • Hermite–Hadamard’s inequality

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