Some generalized fractional integral Simpson’s type inequalities with applications

Sabir Hussain; Javairiya Khalid; Yu Ming Chu; Sabir Hussain; Javairiya Khalid; Yu Ming Chu

doi:10.3934/math.2020375

AIMS Mathematics

2020, Volume 5, Issue 6: 5859-5883. doi: 10.3934/math.2020375

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Research article

Some generalized fractional integral Simpson’s type inequalities with applications

1.
Department of Mathematics, University of Engineering and Technology, Lahore, Pakistan
2.
Department of Mathematics, Huzhou University, Huzhou 313000, P. R. China
3.
Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science & Technology, Changsha 410114, P. R. China

Received: 10 June 2020 Accepted: 08 July 2020 Published: 14 July 2020
MSC : 26D15, 26A51

In the article, we establish a Simpson-type generalized identity containing multi-parameters and derive some new estimates for the generalized Simpson's quadrature rule via the Raina fractional integrals. As applications, we provide several inequalities for the f -divergence measures and probability density functions.
- Simpson’s inequality,
- cumulative distribution function,
- fractional integral,
- f -divergence measure
Citation: Sabir Hussain, Javairiya Khalid, Yu Ming Chu. Some generalized fractional integral Simpson’s type inequalities with applications[J]. AIMS Mathematics, 2020, 5(6): 5859-5883. doi: 10.3934/math.2020375

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Abstract

In the article, we establish a Simpson-type generalized identity containing multi-parameters and derive some new estimates for the generalized Simpson's quadrature rule via the Raina fractional integrals. As applications, we provide several inequalities for the f -divergence measures and probability density functions.

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