Some generalized fractional integral inequalities with nonsingular function as a kernel

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...

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Published inAIMS mathematics Vol. 6; no. 4; pp. 3352 - 3377
Main Authors Mubeen, Shahid, Ali, Rana Safdar, Nayab, Iqra, Rahman, Gauhar, Nisar, Kottakkaran Sooppy, Baleanu, Dumitru
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2021
Subjects
convexity
fractional derivatives and integrals
generalized multi-index bessel function
inequalities and integral operators
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ISSN2473-6988
2473-6988
DOI10.3934/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.
AbstractList 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.
Author Nayab, Iqra
Baleanu, Dumitru
Ali, Rana Safdar
Rahman, Gauhar
Nisar, Kottakkaran Sooppy
Mubeen, Shahid
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  surname: Baleanu
  fullname: Baleanu, Dumitru
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Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40447, Taiwan
Department of Mathematics, University of Lahore, Lahore, Pakistan
Department of Mathematics and Statistics, Hazara University, Mansehra, Pakistan
Department of Mathematics, University of Sargodha, Sargodha, Pakistan
Department of Mathematics, Cankaya University, Ankara 06790, Turkey
Institute of Space Sciences, Magurele-Bucharest 077125, Romania
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Snippet Integral inequalities play a key role in applied and theoretical mathematics. The purpose of inequalities is to develop mathematical techniques in analysis....
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StartPage 3352
SubjectTerms convexity
fractional derivatives and integrals
generalized multi-index bessel function
inequalities and integral operators
Title Some generalized fractional integral inequalities with nonsingular function as a kernel
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