Dynamical significance of generalized fractional integral inequalities via convexity

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...

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Published inAIMS mathematics Vol. 6; no. 9; pp. 9705 - 9730
Main Authors Ali, Sabila, Mubeen, Shahid, Ali, Rana Safdar, Rahman, Gauhar, Morsy, Ahmed, Nisar, Kottakkaran Sooppy, Purohit, Sunil Dutt, Zakarya, M.
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2021
Subjects
fractional inequalities
generalized fractional inequalities
hadamard inequality
wright generalized bessel function
η1
η2)-convex function
Online AccessGet full text
ISSN2473-6988
2473-6988
DOI10.3934/math.2021565

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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.
AbstractList 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.
Author Morsy, Ahmed
Zakarya, M.
Ali, Rana Safdar
Rahman, Gauhar
Mubeen, Shahid
Purohit, Sunil Dutt
Nisar, Kottakkaran Sooppy
Ali, Sabila
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CorporateAuthor Department of Mathematics, University of Lahore, Sargodha Campus, Pakistan
King Khalid University, College of Science, Department of Mathematics, P. O. Box 9004, 61413 Abha, Saudi Arabia
Department of Mathematics, Faculty of Science, Al-Azhar University, 71524 Assiut, Egypt
Department of Mathematics and Statistics, Hazara University, Mansehra, Pakistan
Department of Mathematics, University of Sargodha, Sargodha, Pakistan
Department of Mathematics, College of Arts and Sciences, Wadi Aldawser, 11991, Prince Sattam bin Abdulaziz University, Saudi Arabia
Department of HEAS (Mathematics), Rajasthan Technical University, Kota, India
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Snippet 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...
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SubjectTerms fractional inequalities
generalized fractional inequalities
hadamard inequality
wright generalized bessel function
η1
η2)-convex function
Title Dynamical significance of generalized fractional integral inequalities via convexity
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