Generalized proportional fractional integral functional bounds in Minkowski’s inequalities

Abstract In this research paper, we improve some fractional integral inequalities of Minkowski-type. Precisely, use a proportional operator with respect to another strictly increasing continuous function ? . The functions used in work are bounded by two positive get reverse Minkowski new sense. Moreover, introduce which have close relationship the Minkowski-type via -proportional integral, then help operator, discuss special cases through work. An open issue is covered conclusion section extend current findings be more general.