AUTHOR=Rashid Saima , Hammouch Zakia , Kalsoom Humaira , Ashraf Rehana , Chu Yu Ming 

TITLE=New Investigation on the Generalized K-Fractional Integral Operators

JOURNAL=Frontiers in Physics

VOLUME=8

YEAR=2020

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2020.00025

DOI=10.3389/fphy.2020.00025

ISSN=2296-424X

ABSTRACT=<p>The main objective of this paper is to develop a novel framework to study a new fractional operator depending on a parameter <inline-formula><mml:math id="M2" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi mathvariant="-tex-caligraphic">K</mml:mi></mml:mrow></mml:math></inline-formula> &gt; 0, known as the generalized <inline-formula><mml:math id="M3" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi mathvariant="-tex-caligraphic">K</mml:mi></mml:mrow></mml:math></inline-formula>-fractional integral operator. To ensure appropriate selection and with the discussion of special cases, it is shown that the generalized <inline-formula><mml:math id="M4" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi mathvariant="-tex-caligraphic">K</mml:mi></mml:mrow></mml:math></inline-formula>-fractional integral operator generates other operators. Meanwhile, we derived notable generalizations of the reverse Minkowski inequality and some associated variants by utilizing generalized <inline-formula><mml:math id="M5" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi mathvariant="-tex-caligraphic">K</mml:mi></mml:mrow></mml:math></inline-formula>-fractional integrals. Moreover, two novel results correlate with this inequality, and other variants associated with generalized <inline-formula><mml:math id="M6" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi mathvariant="-tex-caligraphic">K</mml:mi></mml:mrow></mml:math></inline-formula>-fractional integrals are established. Additionally, this newly defined integral operator has the ability to be utilized for the evaluation of many numerical problems.</p>