The Minkowski inequalities via generalized proportional fractional integral operators

• Main Authors: Gauhar Rahman, Aftab Khan, Thabet Abdeljawad, Kottakkaran Sooppy Nisar
• Format: Article
• Language: English
• Published: SpringerOpen 2019-07-01
• Series: Advances in Difference Equations
• Subjects: Minkowski inequalities; Generalized proportional fractional integral operator; Inequality
• Online Access: http://link.springer.com/article/10.1186/s13662-019-2229-7
• ISSN: 1687-1847

Abstract Recent research has gained more attention on conformable integrals and derivatives to derive the various type of inequalities. One of the recent advancements in the field of fractional calculus is the generalized nonlocal proportional fractional integrals and derivatives lately introduced by Jarad et al. (Eur. Phys. J. Special Topics 226:3457–3471, 2017) comprising the exponential functions in the kernels. The principal aim of this paper is to establish reverse Minkowski inequalities and some other fractional integral inequalities by utilizing generalized proportional fractional integrals. Also, two new theorems connected with this inequality as well as other inequalities associated with the generalized proportional fractional integrals are established.