Numerical and visual analysis of Maclaurin type inequalities in the setting of generalized fractional calculus and applications

Yang local fractional calculus is very effective tools to investigate the non-differentiable functions. Moreover, local fractional calculus generalize the classical results and provide more general framework to investigate various problems. This study intends to construct new versions of Maclaurin's inequality for generalized fractional calculus. The study introduces a fresh equation for first-order local differentiable mappings. We develop new error estimates of Maclaurin's inequality incorporated with newly proposed identity, local fractional (L.F) variants of Hölder's type inequalities and generalized convexity. Additionally, we discuss some potential consequences of our primary findings to ensure the worth of our findings. We establish some interesting relations between generalized means, error boundaries of composite quadrature schemes within fractal space and probability distribution. We justify the accuracy of proposed results through visual analysis. The bounds obtained in our study are the better bounds as compared to previously established results. Also, for different values of \({\sigma}\in(0,1]\), blend of inequalities can be obtained.