NEW DEVELOPMENTS IN WEIGHTED n-FOLD TYPE INEQUALITIES VIA DISCRETE GENERALIZED â„ Ì‚-PROPORTIONAL FRACTIONAL OPERATORS

Saima Rashid (), Elbaz I. Abouelmagd (), Sobia Sultana () and Yu-Ming Chu
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Saima Rashid: Department of Mathematics, Government College University, Faisalabad 38000, Pakistan
Elbaz I. Abouelmagd: Celestial Mechanics and Space Dynamics Research Group, Astronomy Department National Research, Institute of Astronomy and Geophysics (NRIAG), Helwan 11421, Cairo, Egypt
Sobia Sultana: Imam Mohammad Ibn Saud Islamic University, Riyadh, KSA, Saudi Arabia
Yu-Ming Chu: Department of Mathematics, Huzhou University, Huzhou 313000, P. R. China5Institute for Advanced Study Honoring, Chen Jian Gong, Hangzhou Normal University, Hangzhou 311121, P. R. China

FRACTALS (fractals), 2022, vol. 30, issue 02, 1-16

Abstract: This study explores some significant consequences of discrete â„ Ì‚-proportional fractional sums (Dâ„ Ì‚PFs) having an exponential function as a nonlocal kernel. Certain novel weighted versions comprising a group of positive mappings via (Dâ„ Ì‚PFs) are given. A variety of refinements can be derived by taking into account the extraction of the new estimates and the nabla â„ Ì‚-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 â„ -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: Discrete Generalized ℠̌-Proportional Fractional Sums/Difference; Integral Inequalities; Nabla/Delta ℠-Fractional Sum/Difference (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22400564

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