Some generalized fractional integral inequalities with nonsingular function as a kernel

Shahid Mubeen; Rana Safdar Ali; Iqra Nayab; Gauhar Rahman; Kottakkaran Sooppy Nisar; Dumitru Baleanu; Shahid Mubeen; Rana Safdar Ali; Iqra Nayab; Gauhar Rahman; Kottakkaran Sooppy Nisar; Dumitru Baleanu

doi:10.3934/math.2021201

AIMS Mathematics

2021, Volume 6, Issue 4: 3352-3377. doi: 10.3934/math.2021201

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Research article

Some generalized fractional integral inequalities with nonsingular function as a kernel

1.
Department of Mathematics, University of Sargodha, Sargodha, Pakistan
2.
Department of Mathematics, University of Lahore, Lahore, Pakistan
3.
Department of Mathematics and Statistics, Hazara University, Mansehra, Pakistan
4.
Department of Mathematics, College of Arts and Sciences, Prince Sattam bin Abdulaziz University, Wadi Aldawser 11991, Saudi Arabia
5.
Department of Mathematics, Cankaya University, Ankara 06790, Turkey
6.
Institute of Space Sciences, Magurele-Bucharest 077125, Romania
7.
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40447, Taiwan

Received: 21 October 2020 Accepted: 06 January 2021 Published: 19 January 2021
MSC : 26A51, 33C10, 26D15, 26A33

Integral inequalities play a key role in applied and theoretical mathematics. The purpose of inequalities is to develop mathematical techniques in analysis. The goal of this paper is to develop a fractional integral operator having a non-singular function (generalized multi-index Bessel function) as a kernel and then to obtain some significant inequalities like Hermit Hadamard Mercer inequality, exponentially $ (s-m) $-preinvex inequalities, Pólya-Szegö and Chebyshev type integral inequalities with the newly developed fractional operator. These results describe in general behave and provide the extension of fractional operator theory (FOT) in inequalities.
- convexity,
- generalized multi-index Bessel function,
- inequalities and integral operators,
- fractional derivatives and integrals
Citation: Shahid Mubeen, Rana Safdar Ali, Iqra Nayab, Gauhar Rahman, Kottakkaran Sooppy Nisar, Dumitru Baleanu. Some generalized fractional integral inequalities with nonsingular function as a kernel[J]. AIMS Mathematics, 2021, 6(4): 3352-3377. doi: 10.3934/math.2021201

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Abstract

Integral inequalities play a key role in applied and theoretical mathematics. The purpose of inequalities is to develop mathematical techniques in analysis. The goal of this paper is to develop a fractional integral operator having a non-singular function (generalized multi-index Bessel function) as a kernel and then to obtain some significant inequalities like Hermit Hadamard Mercer inequality, exponentially $ (s-m) $-preinvex inequalities, Pólya-Szegö and Chebyshev type integral inequalities with the newly developed fractional operator. These results describe in general behave and provide the extension of fractional operator theory (FOT) in inequalities.

References

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