Dynamical significance of generalized fractional integral inequalities via convexity

Sabila Ali; Shahid Mubeen; Rana Safdar Ali; Gauhar Rahman; Ahmed Morsy; Kottakkaran Sooppy Nisar; Sunil Dutt Purohit; M. Zakarya

doi:10.3934/math.2021565

Dynamical significance of generalized fractional integral inequalities via convexity

Sabila Ali, Shahid Mubeen, Rana Safdar Ali, Gauhar Rahman, Ahmed Morsy, Kottakkaran Sooppy Nisar, Sunil Dutt Purohit, M. Zakarya

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16 Scopus citations

Abstract

The main goal of this paper is to develop the significance of generalized fractional integral inequalities via convex functions. We obtain the new version of fractional integral inequalities with the extended Wright generalized Bessel function acting as a kernel for the convex function, which deals with the Hermite-Hadamard type and trapezoid type inequalities. Moreover, we establish new mid-point type and trapezoid type integral inequalities for (η₁, η₂)-convex function related to Hermite-Hadamard type inequality. We establish new version of integral inequality for (η₁, η₂)-convex function related to Fejér type. The results discussed in this paper are a generalized version of many inequalities in literature.

Original language	English
Pages (from-to)	9705-9730
Number of pages	26
Journal	AIMS Mathematics
Volume	6
Issue number	9
DOIs	https://doi.org/10.3934/math.2021565
State	Published - 2021

Keywords

(η, η)-convex function
Fractional inequalities
Generalized fractional inequalities
Hadamard inequality
Wright generalized Bessel function

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10.3934/math.2021565

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title = "Dynamical significance of generalized fractional integral inequalities via convexity",

abstract = "The main goal of this paper is to develop the significance of generalized fractional integral inequalities via convex functions. We obtain the new version of fractional integral inequalities with the extended Wright generalized Bessel function acting as a kernel for the convex function, which deals with the Hermite-Hadamard type and trapezoid type inequalities. Moreover, we establish new mid-point type and trapezoid type integral inequalities for (η1, η2)-convex function related to Hermite-Hadamard type inequality. We establish new version of integral inequality for (η1, η2)-convex function related to Fej{\'e}r type. The results discussed in this paper are a generalized version of many inequalities in literature.",

keywords = "(η, η)-convex function, Fractional inequalities, Generalized fractional inequalities, Hadamard inequality, Wright generalized Bessel function",

author = "Sabila Ali and Shahid Mubeen and Ali, \{Rana Safdar\} and Gauhar Rahman and Ahmed Morsy and Nisar, \{Kottakkaran Sooppy\} and Purohit, \{Sunil Dutt\} and M. Zakarya",

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doi = "10.3934/math.2021565",

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TY - JOUR

T1 - Dynamical significance of generalized fractional integral inequalities via convexity

AU - Ali, Sabila

AU - Mubeen, Shahid

AU - Ali, Rana Safdar

AU - Rahman, Gauhar

AU - Morsy, Ahmed

AU - Nisar, Kottakkaran Sooppy

AU - Purohit, Sunil Dutt

AU - Zakarya, M.

PY - 2021

Y1 - 2021

N2 - The main goal of this paper is to develop the significance of generalized fractional integral inequalities via convex functions. We obtain the new version of fractional integral inequalities with the extended Wright generalized Bessel function acting as a kernel for the convex function, which deals with the Hermite-Hadamard type and trapezoid type inequalities. Moreover, we establish new mid-point type and trapezoid type integral inequalities for (η1, η2)-convex function related to Hermite-Hadamard type inequality. We establish new version of integral inequality for (η1, η2)-convex function related to Fejér type. The results discussed in this paper are a generalized version of many inequalities in literature.

AB - The main goal of this paper is to develop the significance of generalized fractional integral inequalities via convex functions. We obtain the new version of fractional integral inequalities with the extended Wright generalized Bessel function acting as a kernel for the convex function, which deals with the Hermite-Hadamard type and trapezoid type inequalities. Moreover, we establish new mid-point type and trapezoid type integral inequalities for (η1, η2)-convex function related to Hermite-Hadamard type inequality. We establish new version of integral inequality for (η1, η2)-convex function related to Fejér type. The results discussed in this paper are a generalized version of many inequalities in literature.

KW - (η, η)-convex function

KW - Fractional inequalities

KW - Generalized fractional inequalities

KW - Hadamard inequality

KW - Wright generalized Bessel function

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DO - 10.3934/math.2021565

M3 - Article

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JO - AIMS Mathematics

JF - AIMS Mathematics

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ER -

Dynamical significance of generalized fractional integral inequalities via convexity

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