A New k-Fractional Integral Operators and their Applications

Abstract

In this paper, we present a new k-fractional integral oper-ators involving parameters γ, λ analogous to the Riemann-Liouville k-fractional integral. This new fractional integral operators dependent on an exponential function of arbitrary exponent in the kernel of the integral. We prove, certain basic properties such as semi group property, commu-tative law and boundedness for new fractional integral operators. Also, we discuss Chebyshev type inequalities and some k-fractional integral in-equalities corresponding to the new k-fractional integral operators.