Some generalized fractional integral inequalities with nonsingular function as a kernel

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.

Keywords

• convexity
• generalized multi-index bessel function
• inequalities and integral operators
• fractional derivatives and integrals