New developments in fractional integral inequalities via convexity with applications

Maimoona Karim; Aliya Fahmi; Shahid Qaisar; Zafar Ullah; Ather Qayyum; Maimoona Karim; Aliya Fahmi; Shahid Qaisar; Zafar Ullah; Ather Qayyum

doi:10.3934/math.2023814

AIMS Mathematics

2023, Volume 8, Issue 7: 15950-15968. doi: 10.3934/math.2023814

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Research article

New developments in fractional integral inequalities via convexity with applications

1.
Department of Mathematics, University of Faisalabad, Pakistan
2.
Department of Mathematics, COMSATS University Islamabad Sahiwal Campus, Pakistan
3.
Department of Mathematics, University of Education, DGK Campus, Pakistan
4.
Department of Mathematics, Institute of Southern Punjab Multan, Pakistan

Received: 09 December 2022 Revised: 15 March 2023 Accepted: 20 March 2023 Published: 04 May 2023
MSC : 26A33, 26D07, 26D10, 26D15

The main objective of this article is to build up a new integral equality related to Riemann Liouville fractional (RLF) operator. Based on this integral equality, we show numerous new inequalities for differentiable convex as well as concave functions which are similar to celebrated Hermite-Hadamard and Simpson's integral inequalities. The present outcomes of this paper are a unification and generalization of the comparable results in the literature on Hermite-Hadamard and Simpson's integral inequalities. Furthermore as applications in numerical analysis, we find some means, q-digamma function and modified Bessel function type inequalities.
- Simpson's inequality,
- convex functions,
- Riemann-Liouville fractional operator,
- Jensen inequality
Citation: Maimoona Karim, Aliya Fahmi, Shahid Qaisar, Zafar Ullah, Ather Qayyum. New developments in fractional integral inequalities via convexity with applications[J]. AIMS Mathematics, 2023, 8(7): 15950-15968. doi: 10.3934/math.2023814

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Abstract

The main objective of this article is to build up a new integral equality related to Riemann Liouville fractional (RLF) operator. Based on this integral equality, we show numerous new inequalities for differentiable convex as well as concave functions which are similar to celebrated Hermite-Hadamard and Simpson's integral inequalities. The present outcomes of this paper are a unification and generalization of the comparable results in the literature on Hermite-Hadamard and Simpson's integral inequalities. Furthermore as applications in numerical analysis, we find some means, q-digamma function and modified Bessel function type inequalities.

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