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.
Highlights
Fractional calculus is a study of integrals and derivatives of arbitrary order which was a natural outgrowth of conventional definitions of calculus integral and derivative
The idea has been defined by numerous mathematicians with a slightly different formula, for example, Riemann– Liouville, Weyl, Erdélyi–Kober, Hadamard integral, Liouville and Katugampola fractional integral
In the last few years, Khalil et al [24] and Abdeljawad [1] established a new class of fractional derivatives and integrals called fractional conformable derivatives and integrals
Summary
Fractional calculus is a study of integrals and derivatives of arbitrary order which was a natural outgrowth of conventional definitions of calculus integral and derivative. In [20], Jarad et al proposed the left and right generalized nonlocal proportional fractional integral and derivative operators. Such generalizations motivate future research to present more innovative ideas to unify the fractional operators and obtain the inequalities involving such fractional operators. In [10, 45], the authors established the reverse Minkowski inequality for Hadamard fractional integral operators. In [31], Mubeen et al recently established the reverse Minkowski inequalities and some related inequalities for generalized k-fractional conformable integrals. In [13], Dahmani introduced the following reverse Minkowski inequalities involving the R-L fractional integral operators.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
