New Conformable Fractional Integral Inequalities of Hermite–Hadamard Type for Convex Functions

Mohammed, Pshtiwan Othman; Hamasalh, Faraidun K.

doi:10.3390/sym11020263

Cited by 24 publications

(12 citation statements)

References 16 publications

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“…The most important feature of generalized fractional integrals is that they generalize some types of fractional integrals such as Riemann-Liouville fractional integral [1,11,12], k-Riemann-Liouville fractional integral [13], Katugampola fractional integrals [14,15], conformable fractional integral [16], Hadamard fractional integrals [6], and so on. These important special cases of the integral operators (4) and ( 5) are mentioned below:…”

Section: Introductionmentioning

confidence: 99%

On generalized fractional integral inequalities for twice differentiable convex functions

Mohammed

Sarıkaya

2020

Journal of Computational and Applied Mathematics

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In this article, some new generalized fractional integral inequalities of midpoint and trapezoid type for twice differentiable convex functions are obtained. In view of this, we obtain new integral inequalities of midpoint and trapezoid type for twice differentiable convex functions in a form classical integral and Riemann-Liouville fractional integrals. Finally, we apply our new inequalities to construct inequalities involving moments of a continuous random variable.

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Section: Introductionmentioning

confidence: 99%

On generalized fractional integral inequalities for twice differentiable convex functions

Mohammed

Sarıkaya

2020

Journal of Computational and Applied Mathematics

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“…One of the most important applications of fractional integrals is the well known inequality of the Hermite-Hadamard type, see [3,[7][8][9]11,[26][27][28][29][30][31][32][33][34] for more detail.…”

Section: Introductionmentioning

confidence: 99%

On the Generalized Hermite–Hadamard Inequalities via the Tempered Fractional Integrals

2020

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Integral inequality plays a critical role in both theoretical and applied mathematics fields. It is clear that inequalities aim to develop different mathematical methods (numerically or analytically) and to dedicate the convergence and stability of the methods. Unfortunately, mathematical methods are useless if the method is not convergent or stable. Thus, there is a present day need for accurate inequalities in proving the existence and uniqueness of the mathematical methods. Convexity play a concrete role in the field of inequalities due to the behaviour of its definition. There is a strong relationship between convexity and symmetry. Which ever one we work on, we can apply to the other one due to the strong correlation produced between them especially in recent few years. In this article, we first introduced the notion of λ -incomplete gamma function. Using the new notation, we established a few inequalities of the Hermite–Hadamard (HH) type involved the tempered fractional integrals for the convex functions which cover the previously published result such as Riemann integrals, Riemann–Liouville fractional integrals. Finally, three example are presented to demonstrate the application of our obtained inequalities on modified Bessel functions and q-digamma function.

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“…with < a b and ∈ a b , , which can be a significant tool to obtain various priori estimates. Because of its importance, a number of scholars in the field of pure and applied mathematics have dedicated their efforts to extend, generalize, counterpart, and refine the Hermite-Hadamard inequality (2) for different classes of convex functions and mappings, see [20][21][22][23][24][25][26][27][28]. Definition 1.1.…”

Section: Introductionmentioning

confidence: 99%

Generalized fractional integral inequalities of Hermite-Hadamard-type for a convex function

2020

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New Conformable Fractional Integral Inequalities of Hermite–Hadamard Type for Convex Functions

Cited by 24 publications

References 16 publications

On generalized fractional integral inequalities for twice differentiable convex functions

On generalized fractional integral inequalities for twice differentiable convex functions

On the Generalized Hermite–Hadamard Inequalities via the Tempered Fractional Integrals

Generalized fractional integral inequalities of Hermite-Hadamard-type for a convex function

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