Generalized k-Fractional Integral Operators Associated with Polya-Szego and Chebyshev Types Inequalities

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 Polya-Szego type inequalities for Riemann-Liouville and many other fractional integral operators.

Automated summary

Inequalities related to derivatives and integrals are generalized and extended via fractional order integral and derivative operators. This paper aims to define an operator containing Mittag-Leffler function in its kernel to deduce existing well-known operators. By using this generalized operator, some well-known inequalities are studied and it is discovered that the results also apply to Riemann-Liouville and other fractional integral operators.