Graphical illustrations of new inequalities involving Caputo Fabrizio integral operators

Volume 37, Issue 4, pp 373--385 https://dx.doi.org/10.22436/jmcs.037.04.02

Publication Date: November 01, 2024 Submission Date: June 24, 2024 Revision Date: August 26, 2024 Accteptance Date: September 20, 2024

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Authors

M. Tariq - Department of Mathematics and Statistics, University of Lahore, Sargodha campus, Sargodha, Pakistan. A. Nosheen - Department of Mathematics‎, University of Sargodha, Sargodha, Pakistan. Kh. A. Khan - Department of Mathematics‎, University of Sargodha, Sargodha, Pakistan. A. Alburaikan - Department of Mathematics‎, ‎College of Science, ‎Qassim University, ‎Buraydah‎, ‎51452, ‎Saudi Arabia. S. El-Morsy - Department of Mathematics‎, ‎College of Science, ‎Qassim University, ‎Buraydah‎, ‎51452, ‎Saudi Arabia. - Basic Science Department, ‎Nile higher institute for engineering and technology, ‎Mansoura, Egypt.

Abstract

‎In this research study‎, ‎we concentrate on Caputo-Fabrizio operators because of their multiple applications‎. ‎At first‎, ‎we proceed by providing a new identification for this operator‎. ‎Subsequently‎, ‎we use the recently discovered identity to develop a set of integral inequalities via \((s,m)\)-convex function‎. ‎Moreover‎, ‎in the context of integral inequalities‎, ‎we demonstrate how the results enhance and refine a great deal of prior research‎. ‎Later‎, ‎in order to provide an improved comprehension of the recently discovered inequalities‎, ‎we provide particular examples together with the corresponding graphs‎. ‎Our findings build on preceding research and offer insightful perspectives and strategies for addressing various scientific and mathematical issues‎.

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Keywords

• Convex function
• fractional derivative
• fractional integrals
• mathematical operators
• probability theory
• Hermite-Hadamard inequality

MSC

•  26A51
•  26B25
•  46N10
•  26A33

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