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

doi:10.3934/math.2021565

AIMS Mathematics

2021, Volume 6, Issue 9: 9705-9730. doi: 10.3934/math.2021565

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Research article

Dynamical significance of generalized fractional integral inequalities via convexity

1.
Department of Mathematics, University of Lahore, Sargodha Campus, Pakistan
2.
Department of Mathematics, University of Sargodha, Sargodha, Pakistan
3.
Department of Mathematics and Statistics, Hazara University, Mansehra, Pakistan
4.
Department of Mathematics, College of Arts and Sciences, Wadi Aldawser, 11991, Prince Sattam bin Abdulaziz University, Saudi Arabia
5.
Department of HEAS (Mathematics), Rajasthan Technical University, Kota, India
6.
King Khalid University, College of Science, Department of Mathematics, P. O. Box 9004, 61413 Abha, Saudi Arabia
7.
Department of Mathematics, Faculty of Science, Al-Azhar University, 71524 Assiut, Egypt

Received: 30 April 2021 Accepted: 22 June 2021 Published: 28 June 2021
MSC : 26A33, 33C10, 33C20

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 $ (\eta_{1}, \eta_{2}) $-convex function related to Hermite-Hadamard type inequality. We establish new version of integral inequality for $ (\eta_{1}, \eta_{2}) $-convex function related to Fejér type. The results discussed in this paper are a generalized version of many inequalities in literature.
Citation: Sabila Ali, Shahid Mubeen, Rana Safdar Ali, Gauhar Rahman, Ahmed Morsy, Kottakkaran Sooppy Nisar, Sunil Dutt Purohit, M. Zakarya. Dynamical significance of generalized fractional integral inequalities via convexity[J]. AIMS Mathematics, 2021, 6(9): 9705-9730. doi: 10.3934/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 $ (\eta_{1}, \eta_{2}) $-convex function related to Hermite-Hadamard type inequality. We establish new version of integral inequality for $ (\eta_{1}, \eta_{2}) $-convex function related to Fejér type. The results discussed in this paper are a generalized version of many inequalities in literature.

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