On fractional Bullen-type inequalities with applications

Sobia Rafeeq; Sabir Hussain; Jongsuk Ro; Sobia Rafeeq; Sabir Hussain; Jongsuk Ro

doi:10.3934/math.20241198

AIMS Mathematics

2024, Volume 9, Issue 9: 24590-24609. doi: 10.3934/math.20241198

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On fractional Bullen-type inequalities with applications

1.
Department of Basic Sciences and Humanities (Mathematics), MNS University of Engineering and Technology, 60600, Multan, Pakistan
2.
Department of Mathematics, University of Engineering and Technology, 54890, Lahore, Pakistan
3.
School of Electrical and Electronics Engineering, Chung-Ang University, Dongjak-gu, Seoul, 06974, Republic of Korea
4.
Department of Intelligent Energy and Industry, Chung-Ang University, Dongjak-gu, Seoul, 06974, Republic of Korea

Received: 28 June 2024 Revised: 30 July 2024 Accepted: 13 August 2024 Published: 22 August 2024
MSC : 26D15, 26A33, 33C10, 94A17, 60E05

Integral inequalities in mathematical interpretations are a substantial and ongoing body of research. Because fractional calculus techniques are widely used in science, a lot of research has recently been done on them. A key concept in fractional calculus is the Caputo-Fabrizio fractional integral. In this work, we focus on using the Caputo-Fabrizio fractional integral operator to build a multi-parameter fractional integral identity. Using the obtained integral identity, certain generalized estimates of Bullen-type fractional inequalities have been generated. By establishing certain inequalities, this study advances the fields of fractional calculus and convex function research. Both graphical and numerical statistics are provided to show the correctness of our results. We finally provide applications to modified Bessel functions, $ \mathfrak{h} $-divergence measures, and probability density functions.
- Bullen inequality,
- integral operator,
- modified Bessel functions,
- divergence measure,
- probability density function
Citation: Sobia Rafeeq, Sabir Hussain, Jongsuk Ro. On fractional Bullen-type inequalities with applications[J]. AIMS Mathematics, 2024, 9(9): 24590-24609. doi: 10.3934/math.20241198

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Abstract

Integral inequalities in mathematical interpretations are a substantial and ongoing body of research. Because fractional calculus techniques are widely used in science, a lot of research has recently been done on them. A key concept in fractional calculus is the Caputo-Fabrizio fractional integral. In this work, we focus on using the Caputo-Fabrizio fractional integral operator to build a multi-parameter fractional integral identity. Using the obtained integral identity, certain generalized estimates of Bullen-type fractional inequalities have been generated. By establishing certain inequalities, this study advances the fields of fractional calculus and convex function research. Both graphical and numerical statistics are provided to show the correctness of our results. We finally provide applications to modified Bessel functions, $ \mathfrak{h} $-divergence measures, and probability density functions.

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