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NEW ESTIMATES OF INTEGRAL INEQUALITIES VIA GENERALIZED PROPORTIONAL FRACTIONAL INTEGRAL OPERATOR WITH RESPECT TO ANOTHER FUNCTION

SAIMA RASHID

Department of Mathematics, Government College University, Faisalabad, Pakistan

E-mail Address: saimarashid@gcuf.edu.pk

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ZAKIA HAMMOUCH

Faculty of Science and Techniques Moulay Ismail University of Meknes, 52000 Errachidia, Morocco

Department of Mathematics and Science Education, Harran University, Sanliurfa, Turkey

E-mail Address: z.hammouch@fste.umi.ac.ma

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FAHD JARAD

Department of Mathematics, Çankaya University, 06790 Ankara, Turkey

E-mail Address: fahd@cankaya.edu.tr

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, and

YU-MING CHU

Department of Mathematics, Huzhou University, Huzhou 313000, P. R. China

School of Mathematics and Statistics, Changsha University of Science & Technology, Changsha 410114, P. R. China

E-mail Address: chuyuming2005@126.com

Corresponding author.

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https://doi.org/10.1142/S0218348X20400277Cited by:8 (Source: Crossref)

This article is part of the issue:

Special Issue on Fractal and Fractional with Applications to Nature
Guest Editors: Abdon Atangana, Emile Franc Goufo Ndongmo, José Francisco Gómez Aguilar, Muhammad Altaf Khan and Ilknur Koca

Abstract

In this paper, the newly proposed concept of the generalized proportional fractional integral operator with respect to another function $Φ$ has been utilized to generate integral inequalities using convex function. This new concept will have the option to reduce self-similitudes in the fractional attractors under investigation. We discuss the implications and other consequences of the integral inequalities concerning the generalized proportional fractional integral operator with respect to another function $Φ$ are derived here and these outcomes permit us specifically to generalize some classical inequalities. Certain intriguing subsequent consequences of the fundamental hypotheses are also figured. It is to be supposed that this investigation will provide new directions in the quantum theory of capricious nature.

Keywords:

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Vol. 28, No. 08

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History

Received 23 December 2019

Accepted 15 February 2020

Published: June 25, 2020

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This is an Open Access article in the “Special Issue on Fractal and Fractional with Applications to Nature” published by World Scientific Publishing Company. It is distributed under the terms of the Creative Commons Attribution 4.0 (CC BY) License which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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NEW ESTIMATES OF INTEGRAL INEQUALITIES VIA GENERALIZED PROPORTIONAL FRACTIONAL INTEGRAL OPERATOR WITH RESPECT TO ANOTHER FUNCTION

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