GENERALIZING HARDY TYPE INEQUALITIES VIA k-RIEMANN-LIOUVILLE FRACTIONAL INTEGRAL OPERATORS INVOLVING TWO ORDERS

In this study, We have applied the right operator k-Riemann- Liouville is involving two orders α and β with a positive parameter p > 0, further, the left operator k-Riemann-Liouville is used with the negative parameter p < 0 to introduce a new version related to Hardy-type inequalities. These inequalities are given and reversed for the cases 0 < p < 1 and p < 0. We then improved and generalized various consequences in the framework of Hardy-type fractional integral inequalities.