New Generalized Fractional Variants of Integral Inequalities

Abstract

The graphical elegance of fractal theory takes into account the development’s achievability and exceptionalism. Due to its fascinating existence in the mathematical fields of sci- ences, there is a clear association between fractal sets and convexity. In this proposal, we will present generalized convexity and related integral inequalities on a fractal set Rϖ ( 0 < ϖ ≤ 1). In the context of the Beta function, this research presents a new class of gener- alized Hermite-Hadamard type inequalities. This research contributes significant results of novel versions of fractal H¨older’s and Young’s inequalities. We derive some general con- clusions that capture novel results under investigation. One more remarkable contribution of the study is that two novel auxiliary results along with Trapezoidal and Midpoint type inequalities are provided. Hence, these new results will lead us to generalization of prior results.