Dragomir, Sever2021-11-102021-11-102020-06-30https://doi.org/10.31801/cfsuasmas.542665http://hdl.handle.net/20.500.12575/75970Let g be a strictly increasing function on (a,b), having a continuous derivative g′ on (a,b). For the Lebesgue integrable function f:(a,b)→C, we define the k-g-left-sided fractional integral of f by S_{k,g,a+}f(x)=∫_{a}^{x}k(g(x)-g(t))g′(t)f(t)dt, x∈(a,b] and the k-g-right-sided fractional integral of f by S_{k,g,b-}f(x)=∫_{x}^{b}k(g(t)-g(x))g′(t)f(t)dt, x∈[a,b), where the kernel k is defined either on (0,∞) or on [0,∞) with complex values and integrable on any finite 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.enGeneralized Riemann-Liouville fractional integralsHadamard fractional integralsFunctions of bounded variationArticle69149722618-6470