Abstract
In this research, we introduce some new fractional integral inequalities of Minkowski’s type by using Riemann-Liouville fractional integral operator. We replace the constants that appear on Minkowski’s inequality by two positive functions. Further, we establish some new fractional inequalities related to the reverse Minkowski type inequalities via Riemann-Liouville fractional integral. Using this fractional integral operator, some special cases of reverse Minkowski type are also discussed.
Highlights
During their unrelenting eort in the development of mathematics, mathematicians in the past few decades have expanded the concept of classical calculus of derivatives and integrals for integer orders to the fractional calculus, which is a generalized form of classical integrals and derivatives in case of non-integer order
We have presented the reverse Minkowski's inequalities in new generalization through replacing the constants which appear as borders on Minkowski's inequality by two positive functions
We have presented some other related inequalities for reverse Minkowski type inequalities
Summary
During their unrelenting eort in the development of mathematics, mathematicians in the past few decades have expanded the concept of classical calculus of derivatives and integrals for integer orders to the fractional calculus, which is a generalized form of classical integrals and derivatives in case of non-integer order. In (2013), Chinchane with Pachpatte [8] and Taf with Brahim [19], established the reverse Minkowski's inequality via Hadamard fractional integral. In (2018), Vanterler et al [21], presented the reverse Minkowski inequalities and some other related inequalities by mean of Katugampola fractional integral. Our purpose in this paper is to use Riemann-Liouville fractional integral operator to introduce some new fractional integral inequalities of Minkowski's type in case of functional bounds. We establish some new fractional inequalities related to the reverse Minkowski's type inequality via Riemann-Liouville fractional integral operator. We present some other related results involving Riemann-Liouville fractional integral operator
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