Generalized proportional fractional integral functional bounds in Minkowski’s inequalities

Abstract

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

Keywords

• Minkowski inequalities
• Fractional inequalities
• ψ-proportional fractional operators