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Research Article | Open Access

New fractional integral inequalities for preinvex functions involving Caputo-Fabrizio operator

Muhammad Tariq1Hijaz Ahmad2,3Abdul Ghafoor Shaikh4Soubhagya Kumar Sahoo5Khaled Mohamed Khedher6,7Tuan Nguyen Gia8( )
Department of Basic Sciences and Related Studies, Mehran University of Engineering and Technology, Jamshoro 76062, Pakistan
Istanbul Ticaret University, Information Technology Application and Research Center, Istanbul, Turkey
Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy
Department of Basic Sciences and Related Studies, Quest NawabShah, Pakistan
Department of Mathematics, Institute of Technical Education and Research, Siksha 'O' Anusandhan University, Bhubaneswar 751030, Odisha, India
Department of Civil Engineering, College of Engineering, King Khalid University, Abha 61421, Saudi Arabia
Department of acivil Engineering, High Institute of Technological Studies, Mrezgua University Campus, Nebeul 8000, Tunusia
Department of Computing, University of Turku, 20500 Turku, Finland
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Abstract

It's undeniably true that fractional calculus has been the focus point for numerous researchers in recent couple of years. The writing of the Caputo-Fabrizio fractional operator has been on many demonstrating and real-life issues. The main objective of our article is to improve integral inequalities of Hermite-Hadamard and Pachpatte type incorporating the concept of preinvexity with the Caputo-Fabrizio fractional integral operator. To further enhance the recently presented notion, we establish a new fractional equality for differentiable preinvex functions. Then employing this as an auxiliary result, some refinements of the Hermite-Hadamard type inequality are presented. Also, some applications to special means of our main findings are presented.

CLC number: 26A51, 26A33, 26D07, 26D10, 26D15

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AIMS Mathematics
Pages 3440-3455

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Cite this article:
Tariq M, Ahmad H, Shaikh AG, et al. New fractional integral inequalities for preinvex functions involving Caputo-Fabrizio operator. AIMS Mathematics, 2022, 7(3): 3440-3455. https://doi.org/10.3934/math.2022191

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Received: 19 September 2021
Accepted: 18 November 2021
Published: 15 March 2021
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)