Generalized <i>k</i>-Fractional Integral Operators Associated with Pólya-Szegö and Chebyshev Types Inequalities

Abstract

Inequalities related to derivatives and integrals are generalized and extended via fractional order integral and derivative operators. The present paper aims to define an operator containing Mittag-Leffler function in its kernel that leads to deduce many already existing well-known operators. By using this generalized operator, some well-known inequalities are studied. The results of this paper reproduce Chebyshev and Pólya-Szegö type inequalities for Riemann-Liouville and many other fractional integral operators.

Keywords

• Chebyshev inequality
• Pólya-Szegö inequality
• fractional integral operators
• Mittag-Leffler function