The authors discover a general k-fractional integral identity with multi-parameters for twice differentiable functions. By using this integral equation, the authors derive some new bounds on Hermite-Hadamard's and Simpson's inequalities for generalized [Formula: see text]-preinvex functions through k-fractional integrals. By taking the special parameter values for various suitable choices of function h, some interesting results are also obtained.
Keywords: Generalized [Formula: see text]-preinvex functions; Hermite–Hadamard’s inequality; Simpson’s inequality; k-fractional integrals.