A Note on Reverse Minkowski Inequality via Generalized Proportional Fractional Integral Operator with respect to Another Function
Saima Rashid, Fahd Jarad, Yu‐Ming Chu
Abstract
This study reveals new fractional behavior of Minkowski inequality and several other related generalizations in the frame of the newly proposed fractional operators. For this, an efficient technique called generalized proportional fractional integral operator with respect to another function <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mi>Φ</mml:mi></mml:math> is introduced. This strategy usually arises as a description of the exponential functions in their kernels in terms of another function <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mi>Φ</mml:mi></mml:math>. The prime purpose of this study is to provide a new fractional technique, which need not use small parameters for finding the approximate solution of fractional coupled systems and eliminate linearization and unrealistic factors. Numerical results represent that the proposed technique is efficient, reliable, and easy to use for a large variety of physical systems. This study shows that a more general proportional fractional operator is very accurate and effective for analysis of the nonlinear behavior of boundary value problems. This study also states that our findings are more convenient and efficient than other available results.