Some Inequalities of Čebyšev Type for Conformable k-Fractional Integral Operators

Qi, Feng; Rahman, Gauhar; Hussain, Sardar Muhammad; Du, Wei-Shih; Nisar, Kottakkaran Sooppy

doi:10.3390/sym10110614

Cited by 36 publications

(30 citation statements)

References 9 publications

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“…In [35], Aldhaifallah et al introduced some integral inequalities for a certain family of n(n ∈ N) positive continuous and decreasing functions on some intervals employing what is called generalized (k, s)-fractional integral operators. Recently, some researchers introduced a verity of certain interesting inequalities, applications, and properties for the conformable integrals [36][37][38][39][40].…”

Section: Introductionmentioning

confidence: 99%

Bounds of Generalized Proportional Fractional Integrals in General Form via Convex Functions and Their Applications

et al. 2020

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In this paper, our objective is to apply a new approach to establish bounds of sums of left and right proportional fractional integrals of a general type and obtain some related inequalities. From the obtained results, we deduce some new inequalities for classical generalized proportional fractional integrals as corollaries. These inequalities have a connection with some known and existing inequalities which are mentioned in the literature. In addition, some applications of the main results are presented.

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Section: Introductionmentioning

confidence: 99%

Bounds of Generalized Proportional Fractional Integrals in General Form via Convex Functions and Their Applications

et al. 2020

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“…Dahmani [47] presented some classes of fractional integral inequalities by considering a family of n positive functions. Certainly, remarkable inequalities such as Hermite-Hadamard type [48], Chebyshev type [49][50][51], inequalities via generalized conformable integrals [52], Grüss type [53,54], fractional proportional inequalities and inequalities for convex functions [55], Hadamard proportional fractional integrals [56], bounds of proportional integrals with applications [57], inequalities for the weighted and the extended Chebyshev functionals [58], certain new inequalities for a class of n(n ∈ N) positive continuous and decreasing functions [59] and certain generalized fractional inequalities [60] are recently presented by utilizing several different kinds of fractional calculus approaches.…”

Section: Introductionmentioning

confidence: 99%

Tempered Fractional Integral Inequalities for Convex Functions

2020

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Certain new inequalities for convex functions by utilizing the tempered fractional integral are established in this paper. We also established some new results by employing the connections between the tempered fractional integral with the (R-L) fractional integral. Several special cases of the main result are also presented. The obtained results are more in a general form as it reduced certain existing results of Dahmani (2012) and Liu et al. (2009) by employing some particular values of the parameters.

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“…In [1], the authors established fractional integral inequalities for a class of family of n (n ∈ N) positive continuous and decreasing functions on [a, b] by employing the (k, s)-fractional integral operators. Recently the authors [10,21,26,27] introduced various types of inequalities by employing the fractional conformable integrals.…”

Section: Introductionmentioning

confidence: 99%

Some fractional proportional integral inequalities

et al. 2019

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In the last few years, various researchers studied the so-called conformable integrals and derivatives. Based on that notion some authors used modified conformable derivatives (proportional derivatives) to generate nonlocal fractional integrals and derivatives, called fractional proportional integrals and derivatives, which contain exponential functions in their kernels. Our aim in this paper is to establish some new integral inequalities by utilizing the fractional proportional-integral operators. In fact, certain new classes of integral inequalities for a class of n (n ∈ N) positive continuous and decreasing functions on [a, b] are presented. The inequalities presented in this paper are more general than the existing classical inequalities.

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Some Inequalities of Čebyšev Type for Conformable k-Fractional Integral Operators

Abstract: In the article, the authors present several inequalities of the Čebyšev type for conformable k-fractional integral operators.

Cited by 36 publications

References 9 publications

Bounds of Generalized Proportional Fractional Integrals in General Form via Convex Functions and Their Applications

Bounds of Generalized Proportional Fractional Integrals in General Form via Convex Functions and Their Applications

Tempered Fractional Integral Inequalities for Convex Functions

Some fractional proportional integral inequalities

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