Fractal-Fractional reverse Minkowski type generalizations and related results

Abstract

Fractional inequalities have recently gained prominence and have been the focus of numerous research studies. The effects of various sorts of inequalities have been analyzed by identifying revolutionary methodological approaches and implementations. This research determined reverse Minkowski inequalities using fractal-fractional integral operators, which furnishes both pragmatic and influential outcomes. In this paper, new differentiation operators, such as the convolution of the index kernel, the exponential decay, and the generalized Mittag-Leffler kernel with fractal derivative, have been implemented for classical Minkowski type inequalities. Moreover, we obtain several inequalities as particular cases of the main outcomes and these generalizations. We carried out a variety of inequalities using the fractal-fractional formulation strategy and achieved several interesting results in terms of (i) varying fractional order and fixing fractal-dimension, (iii) varying fractional-order and fixing fractal-dimension, and (iii) varying both fractional-order and fractal-dimension, respectively. The study findings leave no doubt that this notion is a new window that will assist mankind in a deeper understanding of nature.