Inequalities by Means of Generalized Proportional Fractional Integral Operators with Respect to Another Function

Rashid, Saima; Jarad, Fahd; Noor, Muhammad Aslam; Kalsoom, Humaira; Chu, Yu‐Ming

doi:10.3390/math7121225

Cited by 86 publications

(45 citation statements)

References 25 publications

(27 reference statements)

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“…The continuous growth of interest has occurred in order to meet the requirements in needs of fertile applications of these inequalities. Such inequalities had been studied by many researchers who in turn used various techniques for the sake of exploring and offering these inequalities [31][32][33][34][35][36][37][38][39][40][41][42] and the references cited therein.…”

Section: Fuzzy Structures Functions Limitations On Functionsmentioning

confidence: 99%

T-Spherical Fuzzy Einstein Hybrid Aggregation Operators and Their Applications in Multi-Attribute Decision Making Problems

et al. 2020

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T-spherical fuzzy set is a recently developed model that copes with imprecise and uncertain events of real-life with the help of four functions having no restrictions. This article’s aim is to define some improved algebraic operations for T-SFSs known as Einstein sum, Einstein product and Einstein scalar multiplication based on Einstein t-norms and t-conorms. Then some geometric and averaging aggregation operators have been established based on defined Einstein operations. The validity of the defined aggregation operators has been investigated thoroughly. The multi-attribute decision-making method is described in the environment of T-SFSs and is supported by a comprehensive numerical example using the proposed Einstein aggregation tools. As consequences of the defined aggregation operators, the same concept of Einstein aggregation operators has been proposed for q-rung orthopair fuzzy sets, spherical fuzzy sets, Pythagorean fuzzy sets, picture fuzzy sets, and intuitionistic fuzzy sets. To signify the importance of proposed operators, a comparative analysis of proposed and existing studies is developed, and the results are analyzed numerically. The advantages of the proposed study are demonstrated numerically over the existing literature with the help of examples.

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Section: Fuzzy Structures Functions Limitations On Functionsmentioning

confidence: 99%

T-Spherical Fuzzy Einstein Hybrid Aggregation Operators and Their Applications in Multi-Attribute Decision Making Problems

et al. 2020

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“…One of the aspects which are nowadays particularly well known among researchers is the integral inequalities with applications. In this field, the majority of the authors are generalizing the standard results in the accessible literature by utilizing various sorts/definitions of the fractional integral operators [4,25,50,51]. An enormous heft of fractional differential problems and partial differential equations can be converted into problems of comprehending some estimated integral equations.…”

Section: Introductionmentioning

confidence: 99%

Some new Simpson-type inequalities for generalized p-convex function on fractal sets with applications

et al. 2020

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The present article addresses the concept of p-convex functions on fractal sets. We are able to prove a novel auxiliary result. In the application aspect, the fidelity of the local fractional is used to establish the generalization of Simpson-type inequalities for the class of functions whose local fractional derivatives in absolute values at certain powers are p-convex. The method we present is an alternative in showing the classical variants associated with generalized p-convex functions. Some parts of our results cover the classical convex functions and classical harmonically convex functions. Some novel applications in random variables, cumulative distribution functions and generalized bivariate means are obtained to ensure the correctness of the present results. The present approach is efficient, reliable, and it can be used as an alternative to establishing new solutions for different types of fractals in computer graphics.

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“…Fractional integral inequalities are an appropriate device for enhancing the qualitative and quantitative properties of differential equations. There has been a continuous growth of interest in several areas of science: mathematics, physics, engineering, amongst others, and particularly, initial value problems, linear transformation stability, integral-differential equations, and impulse equations [23][24][25][26][27][28][29][30].…”

Section: Introductionmentioning

confidence: 99%

New Investigation on the Generalized K-Fractional Integral Operators

et al. 2020

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The main objective of this paper is to develop a novel framework to study a new fractional operator depending on a parameter K > 0, known as the generalized K-fractional integral operator. To ensure appropriate selection and with the discussion of special cases, it is shown that the generalized K-fractional integral operator generates other operators. Meanwhile, we derived notable generalizations of the reverse Minkowski inequality and some associated variants by utilizing generalized K-fractional integrals. Moreover, two novel results correlate with this inequality, and other variants associated with generalized K-fractional integrals are established. Additionally, this newly defined integral operator has the ability to be utilized for the evaluation of many numerical problems.

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Inequalities by Means of Generalized Proportional Fractional Integral Operators with Respect to Another Function

Cited by 86 publications

References 25 publications

T-Spherical Fuzzy Einstein Hybrid Aggregation Operators and Their Applications in Multi-Attribute Decision Making Problems

T-Spherical Fuzzy Einstein Hybrid Aggregation Operators and Their Applications in Multi-Attribute Decision Making Problems

Some new Simpson-type inequalities for generalized p-convex function on fractal sets with applications

New Investigation on the Generalized K-Fractional Integral Operators

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