Some new bounds analogous to generalized proportional fractional integral operator with respect to another function

Saima Rashid; Fahd Jarad; Zakia Hammouch

doi:10.3934/dcdss.2021020

Article Contents

2021, Volume 14, Issue 10: 3703-3718. Doi: 10.3934/dcdss.2021020

This issue Previous Article Numerical simulation of the nonlinear fractional regularized long-wave model arising in ion acoustic plasma waves Next Article Comprehensive analysis of integer-order, Caputo-Fabrizio (CF) and Atangana-Baleanu (ABC) fractional time derivative for MHD Oldroyd-B fluid with slip effect and time dependent boundary condition

Some new bounds analogous to generalized proportional fractional integral operator with respect to another function

1.
Government College University, Faisalabad, Pakistan
2.
Department of Mathematics, Faculty of Arts and Sciences, Cankaya University Ankara, Turkey
3.
Department of Medical Research, China Medical University Hospital, Taichung 40402, Taiwan, École Normale Supérieure, Moulay Ismail University, Meknes, Morocco

^* Corresponding author: Zakia Hammouch.
^* Corresponding author: Zakia Hammouch.

Received: November 2019

Revised: January 2020

Early access: March 2021

Published: October 2021

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Abstract

The present article deals with the new estimates in the view of generalized proportional fractional integral with respect to another function. In the present investigation, we focus on driving certain new classes of integral inequalities utilizing a family of positive functions $ n(n\in\mathbb{N}) $ for this newly defined operator. From the computed outcomes, we concluded some new variants for classical generalized proportional fractional and other integrals as remarks. These variants are connected with some existing results in the literature. Certain interesting consequent results of the main theorems are also pointed out.

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Mathematics Subject Classification: Primary: 26D10; 26D15; 26A33.

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