Some generalized fractional integral inequalities with nonsingular function as a kernel

• Published in: AIMS 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
• Language: English
• Published: AIMS Press 01.01.2021
• Subjects: convexity; fractional derivatives and integrals; generalized multi-index bessel function; inequalities and integral operators
• ISSN: 2473-6988; 2473-6988
• DOI: 10.3934/math.2021201

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.