On Minkowski Inequalities Involving Fractional Calculus With General Analytic Kernels

2023/10/17 by Erdal Gül, Gül, Erdal, Ahmet Ocak Akdemi̇r +3
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Inequalities and Applications #Mathematical functions and polynomials #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2310.11221

openalex publication_date 2023/10/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

There have been many proposed forms of fractional calculus, which can be grouped into a few broad classes of operators. By replacing the kernel of the power function with another kernel function, the traditional Riemann-Liouville formula and its generalisations are modified. Recent research has focused on Minkowski fractional inequalities and other inequalities for fractional integrals of certain types of functions. We also provide many concrete examples of applications to demonstrate the power of our key findings. It is no longer necessary to prove such statements separately for each model. This is because in a single study we have provided theorems that are valid for the entire general class of fractional operators. We can also study fractional integrals and derivatives with respect to functions.

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