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

Muhammad Tariq; Hijaz Ahmad; Abdul Ghafoor Shaikh; Soubhagya Kumar Sahoo; Khaled Mohamed Khedher; Tuan Nguyen Gia; Muhammad Tariq; Hijaz Ahmad; Abdul Ghafoor Shaikh; Soubhagya Kumar Sahoo; Khaled Mohamed Khedher; Tuan Nguyen Gia

doi:10.3934/math.2022191

AIMS Mathematics

2022, Volume 7, Issue 3: 3440-3455. doi: 10.3934/math.2022191

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Research article

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

1.
Department of Basic Sciences and Related Studies, Mehran University of Engineering and Technology, Jamshoro 76062, Pakistan
2.
Istanbul Ticaret University, Information Technology Application and Research Center, Istanbul, Turkey
3.
Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy
4.
Department of Basic Sciences and Related Studies, Quest NawabShah, Pakistan
5.
Department of Mathematics, Institute of Technical Education and Research, Siksha 'O' Anusandhan University, Bhubaneswar 751030, Odisha, India
6.
Department of Civil Engineering, College of Engineering, King Khalid University, Abha 61421, Saudi Arabia
7.
Department of acivil Engineering, High Institute of Technological Studies, Mrezgua University Campus, Nebeul 8000, Tunusia
8.
Department of Computing, University of Turku, 20500 Turku, Finland

Received: 19 September 2021 Accepted: 18 November 2021 Published: 01 December 2021
MSC : 26A51, 26A33, 26D07, 26D10, 26D15

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.
- Caputo-Fabrizio fractional integral,
- preinvex functions,
- Hermite-Hadamard inequality,
- Hölder inequality,
- Hölder-İşcan inequality,
- Power-mean inequality
Citation: Muhammad Tariq, Hijaz Ahmad, Abdul Ghafoor Shaikh, Soubhagya Kumar Sahoo, Khaled Mohamed Khedher, Tuan Nguyen Gia. New fractional integral inequalities for preinvex functions involving Caputo-Fabrizio operator[J]. AIMS Mathematics, 2022, 7(3): 3440-3455. doi: 10.3934/math.2022191

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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.

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