Inequalities presenting error bounds for trapezoidal formula using Caputo-Fabrizio integrals via convex functions with graphical depiction

Volume 34, Issue 1, pp 85--98 https://dx.doi.org/10.22436/jmcs.034.01.08

Publication Date: February 23, 2024 Submission Date: October 10, 2023 Revision Date: December 04, 2023 Accteptance Date: January 04, 2024

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Authors

A. Nosheen - Department of Mathematics, University of Sargodha, Sargodha, Pakistan. M. Tariq - Department of Mathematics and Statistics, University of Lahore, Sargodha campus, Sargodha, Pakistan. Kh. A. Khan - Department of Mathematics, University of Sargodha, Sargodha, Pakistan. S. El-Morsy - Department of Mathematics, College of Science and Arts, Al-Badaya 51951, Qassim University, Saudi Arabia. - Basic Science Department, Nile Higher Institute for Engineering and Technology, Mansoura, Egypt.

Abstract

This paper accomplishes some new Hermite-Hadamard type inequalities for \((\alpha,s,m)\)-convex functions in the context of Caputo-Fabrizio integrals. We establish this new version with the aid of Hölder and power-mean inequalities. Applications to obtained results are given by special means. Furthermore, errors are estimated for the trapezoidal formula and are graphically depicted. Finally, some bounds for the expectation value of the probability density function (which is \((\alpha,s,m)\)-convex) are obtained using the exponential population growth model.

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Keywords

• Convex function
• Hölder's inequality
• power-mean inequality
• fractional derivatives
• probability density function
• optimization

MSC

•  26A51
•  26B25
•  46N10
•  26A33

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