Benaissa, BouharketBudak, Huseyin2025-10-112025-10-1120241787-24051787-2413https://doi.org/10.18514/MMN.2024.4594https://hdl.handle.net/20.500.12684/21666The main motivation of this study is to establish a general version of the RiemannLiouville fractional integrals with two exponential parameters k and p called ((k, p),psi)-Hilfer fractional integrals which is determined over the k-gamma function. We first prove that these operators are well-defined, continuous and have semi-group property. Then, particularly, we present the harmonic, geometric and arithmetic (k, p), psi-Hilfer fractional integrals. Moreover, some special cases relating to general ((k, p),psi)-Riemann-Liouville fraction integrals are given.en10.18514/MMN.2024.4594info:eu-repo/semantics/openAccess((k, p ) , psi)-Hilfer fractionalk-gamma functionRiemann-Liouville operatorHadam- ard operatorKatugampola operatorArticle2522-s2.0-85212327308WOS:001402251100007Q2Q2