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

Volume 38, Issue 3, pp 281--297 https://dx.doi.org/10.22436/jmcs.038.03.01

Publication Date: December 13, 2024 Submission Date: August 04, 2024 Revision Date: August 26, 2024 Accteptance Date: October 28, 2024

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Authors

Y. Wang - School of Mathematical Sciences, Zhejiang Normal University, Jinhua 321004, China. U. Asif - Department of Mathematics, Government College University Faisalabad, Pakistan. M. Z. Javed - Department of Mathematics, Government College University Faisalabad, Pakistan. M. U. Awan - Department of Mathematics, Government College University Faisalabad, Pakistan. B. Meftah - Laboratory of Analysis and Control of Differential Equations 'ACED', Department of Mathematics, University of 8 May 1945, Guelma 24000, Algeria. A. Kashuri - Department of Mathematical Engineering, Polytechnic University of Tirana, Tirana 1001, Albania. M. A. Noor - Department of Mathematics, COMSATS University Islamabad, Islamabad, Pakistan.

Abstract

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.

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Keywords

• Convex functions
• Maclaurin inequality
• Hölder's inequality
• Newton-Cotes formula
• local fractional

MSC

•  26D10
•  26A33
•  26D15
•  26A51

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