Extensions of different type parameterized inequalities for generalized [Formula: see text]-preinvex mappings via -fractional integrals.

The authors discover a general -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 -fractional integrals. By taking the special parameter values for various suitable choices of function , some interesting results are also obtained.