GENERAL ((k, p ) , ψ)-HILFER FRACTIONAL INTEGRALS

The 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.