Further inequalities for the generalized k-g-fractional integrals of functions with bounded variation

Abstract

Let g be a strictly increasing function on (a; b) ; having a continuous derivative g 0 on (a; b) : For the Lebesgue integrable function f : (a; b) ! C, we de…ne the k-g-left-sided fractional integral of f bywhere the kernel k is de…ned either on (0; 1) or on [0; 1) with complex values and integrable on any …nite subinterval.In this paper we establish some new inequalities for the k-g-fractional integrals of functions of bounded variation.Examples for the generalized left-and right-sided Riemann-Liouville fractional integrals of a function f with respect to another function g and a general exponential fractional integral are also provided.