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NEW GENERALIZATION INVOLVING CONVEX FUNCTIONS VIA $ℏ$ -DISCRETE $𝒜 ℬ$ -FRACTIONAL SUMS AND THEIR APPLICATIONS IN FRACTIONAL DIFFERENCE EQUATIONS

SAIMA RASHID

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

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

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AASMA KHALID

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

E-mail Address: aasmakhalid@gcwuf.edu.pk

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YELIZ KARACA

University of Massachusetts Medical School, Worcester, MA 01655, USA

E-mail Address: yeliz.karaca@ieee.org

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ZAKIA HAMMOUCH

Division of Applied mathematics, Thu Dau Mot University, Binh Duong Province, Vietnam

E-mail Address: hammouch.zakia@tdmu.edu.vn

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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/S0218348X2240134XCited by:9 (Source: Crossref)

This article is part of the issue:

Special Issue on Fractal AI-Based Analyses and Applications to Complex Systems: Part III
Lead Guest Editors: Yeliz Karaca & Dumitru Baleanu
Guest Editors: Majaz Moonis, Yu-Dong Zhang & Osvaldo Gervasi

Abstract

The purpose of this paper is to explore novel variants for convex functions via discrete $𝒜 ℬ$ -fractional operator in the frame of time scale calculus $ℏ ℤ$ with $0 < α < 1$ and $0 < ℏ \leq 1 .$ Based on a comparison with the integral inequalities, we have provided new discrete fractional inequalities having $ℏ$ -discrete generalized Mittag-Leffler function in the kernel which generates several known results and can be utilized as handy tools in the investigation of qualitative and quantitative properties of solutions of certain classes of difference equations. Several new special cases are also apprehended in the setting of time scale $ℤ$ and $𝕋 .$ As the application aspect, we provide an illustrated example to show the effectiveness of our new criteria in fractional $ℏ$ -difference type initial value problem.

Keywords:

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Vol. 30, No. 05

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History

Received 18 June 2021

Accepted 23 November 2021

Published: May 27, 2022

Information

This is an Open Access article in the “Special Issue Section on Fractal AI-Based Analyses and Applications to Complex Systems: Part III”, edited by Yeliz Karaca (University of Massachusetts Medical School, USA), Dumitru Baleanu (Cankaya University, Turkey), Majaz Moonis (University of Massachusetts Medical School, USA), Yu-Dong Zhang (University of Leicester, UK) & Osvaldo Gervasi (Perugia University, Italy) published by World Scientific Publishing Company. It is distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 (CC-BY-NC-ND) License which permits use, distribution and reproduction in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.

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