Ostrowski type inequalities in the sense of generalized $\mathcal{K}$-fractional integral operator for exponentially convex functions

Rashid, Saima; Noor, Muhammad Aslam; Noor, Khalida İnayat; Chu, Yu‐Ming

doi:10.3934/math.2020171

Cited by 75 publications

(28 citation statements)

References 27 publications

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“…In particular, they have been successfully used in the study of fractional differential equations and sometimes called fractional integral inequalities. They have been vital in proving the uniqueness or existence of solutions for some well-known fractional differential equations and in providing boundedness to solve certain fractional boundary and initial value problems, see for detail [1,7,19,24,26,33,34,41,[48][49][50][51]. The rest of the article is organized as follows: In Sect.…”

Section: Introductionmentioning

confidence: 99%

Integral inequalities for a fractional operator of a function with respect to another function with nonsingular kernel

Mohammed

Abdeljawad

2020

Adv Differ Equ

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At first, we construct a connection between the Atangana-Baleanu and the Riemann-Liouville fractional integrals of a function with respect to a monotone function with nonsingular kernel. By examining this relationship and the iterated form of Prabhakar fractional model, we are able to find some new Hermite-Hadamard inequalities and related results on integral inequalities for the two models of fractional calculus which are defined using monotone functions with nonsingular kernels.

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Section: Introductionmentioning

confidence: 99%

Integral inequalities for a fractional operator of a function with respect to another function with nonsingular kernel

Mohammed

Abdeljawad

2020

Adv Differ Equ

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“…For a concave function H, the inequalities in (1.1) hold in reverse direction. Over the last two decades, these types of generalizations have led to many novel testimonies, stimulating extensions, conspicuous generalizations, innovative HHtype inequalities, and a lot of applications of inequalities (1.1) in the literature of mathematical inequalities and in other branches of pure and applied mathematics; see [28][29][30] and the references therein.…”

Section: Introduction and Prelimnariesmentioning

confidence: 99%

Some new local fractional inequalities associated with generalized $(s,m)$-convex functions and applications

et al. 2020

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Fractal analysis is one of interesting research areas of computer science and engineering, which depicts a precise description of phenomena in modeling. Visual beauty and self-similarity has made it an attractive field of research. The fractal sets are the effective tools to describe the accuracy of the inequalities for convex functions. In this paper, we employ linear fractals R α to investigate the (s, m)-convexity and relate them to derive generalized Hermite-Hadamard (HH) type inequalities and several other associated variants depending on an auxiliary result. Under this novel approach, we aim at establishing an analog with the help of local fractional integration. Meanwhile, we establish generalized Simpson-type inequalities for (s, m)-convex functions. The results in the frame of local fractional showed that among all comparisons, we can only see the correlation between novel strategies and the earlier consequences in generalized s-convex, generalized m-convex, and generalized convex functions. We obtain application in probability density functions and generalized special means to confirm the relevance and computational effectiveness of the considered method. Similar results in this dynamic field can also be widely applied to other types of fractals and explored similarly to what has been done in this paper.

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“…Inequality plays an irreplaceable role in the development of mathematics. Very recently, many new inequalities such as Hermite-Hadamard type inequality [34][35][36][37][38], Petrović type inequality [39], Pólya-Szegö type inequality [40], Ostrowski type inequality [41], reverse Minkowski inequality [42], Jensen type inequality [43,44], Bessel function inequality [45], trigonometric and hyperbolic function inequalities [46], fractional integral inequality [47][48][49][50][51], complete and generalized elliptic integral inequalities [52][53][54][55][56][57], generalized convex function inequality [58][59][60], and mean value inequality [61][62][63] have been discovered by many researchers. In particular, the applications of integral inequalities have gained considerable importance among researchers for fixed-point theorems; the existence and uniqueness of solutions for differential equations [64][65][66][67][68] and numerous numerical and analytical methods have been recommended for the advancement of integral inequalities [69][70][71][72][73][74]…”

Section: Introductionmentioning

confidence: 99%

On New Modifications Governed by Quantum Hahn’s Integral Operator Pertaining to Fractional Calculus

Rashid

Khalid

Rahman

et al. 2020

Journal of Function Spaces

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In the article, we present several generalizations for the generalized Čebyšev type inequality in the frame of quantum fractional Hahn’s integral operator by using the quantum shift operator σΨqς=qς+1−qσς∈l1,l2,σ=l1+ω/1−q,0<q<1,ω≥0. As applications, we provide some associated variants to illustrate the efficiency of quantum Hahn’s integral operator and compare our obtained results and proposed technique with the previously known results and existing technique. Our ideas and approaches may lead to new directions in fractional quantum calculus theory.

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Ostrowski type inequalities in the sense of generalized $\mathcal{K}$-fractional integral operator for exponentially convex functions

Cited by 75 publications

References 27 publications

Integral inequalities for a fractional operator of a function with respect to another function with nonsingular kernel

Integral inequalities for a fractional operator of a function with respect to another function with nonsingular kernel

Some new local fractional inequalities associated with generalized $(s,m)$-convex functions and applications

On New Modifications Governed by Quantum Hahn’s Integral Operator Pertaining to Fractional Calculus

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