Interval valued Hadamard-Fejér and Pachpatte Type inequalities pertaining to a new fractional integral operator with exponential kernel

Hari Mohan Srivastava; Soubhagya Kumar Sahoo; Pshtiwan Othman Mohammed; Bibhakar Kodamasingh; Kamsing Nonlaopon; Khadijah M. Abualnaja; Hari Mohan Srivastava; Soubhagya Kumar Sahoo; Pshtiwan Othman Mohammed; Bibhakar Kodamasingh; Kamsing Nonlaopon; Khadijah M. Abualnaja

doi:10.3934/math.2022824

AIMS Mathematics

2022, Volume 7, Issue 8: 15041-15063. doi: 10.3934/math.2022824

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Interval valued Hadamard-Fejér and Pachpatte Type inequalities pertaining to a new fractional integral operator with exponential kernel

1.
Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada
2.
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
3.
Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, AZ1007 Baku, Azerbaijan
4.
Section of Mathematics, International Telematic University Uninettuno, I-00186 Rome, Italy
5.
Department of Mathematics, Institute of Technical Education and Research, Siksha 'O' Anusandhan University, Bhubaneswar 751030, India
6.
Department of Mathematics, College of Education, University of Sulaimani, Sulaimani 46001, Iraq
7.
Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand
8.
Department of Mathematics and Statistics, College of Science, Taif University, P. O. Box 11099, Taif 21944, Saudi Arabia

Received: 21 April 2022 Revised: 29 May 2022 Accepted: 09 June 2022 Published: 14 June 2022
MSC : 26A51, 26A33, 26D10

The aim of this research is to combine the concept of inequalities with fractional integral operators, which are the focus of attention due to their properties and frequency of usage. By using a novel fractional integral operator that has an exponential function in its kernel, we establish a new Hermite-Hadamard type integral inequality for an LR-convex interval-valued function. We also prove new fractional-order variants of the Fejér type inequalities and the Pachpatte type inequalities in the setting of pseudo-order relations. By showing several numerical examples, we further validate the accuracy of the results that we have derived in this study. We believe that the results, presented in this article are novel and that they will be beneficial in encouraging future research in this field.
- LR-convex interval-valued function,
- fractional integral operator,
- Hermite–Hadamard type inequality,
- Pachpatte type inequality,
- Fejér type inequality,
- exponential kernel
Citation: Hari Mohan Srivastava, Soubhagya Kumar Sahoo, Pshtiwan Othman Mohammed, Bibhakar Kodamasingh, Kamsing Nonlaopon, Khadijah M. Abualnaja. Interval valued Hadamard-Fejér and Pachpatte Type inequalities pertaining to a new fractional integral operator with exponential kernel[J]. AIMS Mathematics, 2022, 7(8): 15041-15063. doi: 10.3934/math.2022824

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Abstract

The aim of this research is to combine the concept of inequalities with fractional integral operators, which are the focus of attention due to their properties and frequency of usage. By using a novel fractional integral operator that has an exponential function in its kernel, we establish a new Hermite-Hadamard type integral inequality for an LR-convex interval-valued function. We also prove new fractional-order variants of the Fejér type inequalities and the Pachpatte type inequalities in the setting of pseudo-order relations. By showing several numerical examples, we further validate the accuracy of the results that we have derived in this study. We believe that the results, presented in this article are novel and that they will be beneficial in encouraging future research in this field.

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