Ostrowski and Trapezoid Type Inequalities for the Generalized <em>k</em>-<em>g</em>-Fractional Integrals of Functions with Bounded Variation

Abstract

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 byand the k-g-right-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 Ostrowski and trapezoid type inequalities for the k-g-fractional integrals of functions of bounded variation. Applications for mid-point and trapezoid inequalities are provided as well. Some examples for a general exponential fractional integral are also given.