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NEW DEVELOPMENTS IN WEIGHTED $n$ $n$ -FOLD TYPE INEQUALITIES VIA DISCRETE GENERALIZED $\hat{ℏ}$ -PROPORTIONAL FRACTIONAL OPERATORS

Department of Mathematics, Government College University, Faisalabad 38000, Pakistan

Celestial Mechanics and Space Dynamics Research Group, Astronomy Department National Research, Institute of Astronomy and Geophysics (NRIAG), Helwan 11421, Cairo, Egypt

E-mail Address: elbaz.abouelmagd@nriag.sci.eg

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SOBIA SULTANA

Imam Mohammad Ibn Saud Islamic University, Riyadh, KSA, Saudi Arabia

E-mail Address: ssmahmood@imamu.edu.sa

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, and

YU-MING CHU

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

Institute for Advanced Study Honoring, Chen Jian Gong, Hangzhou Normal University, Hangzhou 311121, P. R. China

E-mail Address: chuyuming@zjhu.edu.cn

Corresponding author.

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https://doi.org/10.1142/S0218348X22400564Cited by:57 (Source: Crossref)

This article is part of the issue:

Special Issue on Dynamical Systems and Their Applications to Engineering, Economy and Health Sciences
Guest Editors: Juan L. G. Guirao, Elbaz I. Abouelmagd and Bruce A. Wade

Abstract

This study explores some significant consequences of discrete $\hat{ℏ}$ -proportional fractional sums $(D \hat{ℏ} P F s)$ having an exponential function as a nonlocal kernel. Certain novel weighted versions comprising a group of positive mappings via $(D \hat{ℏ} P F s)$ are given. A variety of refinements can be derived by taking into account the extraction of the new estimates and the nabla $\hat{ℏ}$ -fractional sums. The suggested technique is a revolutionary formulation of conventional operators that may be used to design efficient mechanism descriptions in short time spans by provoking certain noteworthy properties of chaos theory. Moreover, novel generalizations of the discrete $ℏ$ -fractional sum can be generated by the specific value of the proportionality index. Derived outcomes and investigation confirm that the proposed plan will offer gains in many modeling and chaotic framework applications.

Keywords:

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Vol. 30, No. 02

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History

Received 8 March 2021

Accepted 7 August 2021

Published: March 12, 2022

Information

This is an Open Access article in the “Special Issue on Dynamical Systems and Their Applications to Engineering, Economy and Health Sciences”, edited by Juan L.G. Guirao (Technical University of Cartagena, Spain), Elbaz I. Abouelmagd (National Research Institute of Astronomy and Geophysics (NRIAG), Cairo, Egypt) & Bruce A. Wade (University of Louisiana at Lafayette, USA) 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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