Analysing Milne-type inequalities by using tempered fractional integrals

Haider, Wali; Budak, HÜSEYİN; Shehzadi, Asia; Hezenci, Fatih; Chen, Haibo

doi:10.1007/s13324-024-00958-3

Analysing Milne-type inequalities by using tempered fractional integrals

Haider W., Budak H., Shehzadi A., Hezenci F., Chen H.

ANALYSIS AND MATHEMATICAL PHYSICS, vol.14, no.5, 2024 (SCI-Expanded, Scopus)

Publication Type: Article / Article
Volume: 14 Issue: 5
Publication Date: 2024
Doi Number: 10.1007/s13324-024-00958-3
Journal Name: ANALYSIS AND MATHEMATICAL PHYSICS
Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
Kocaeli University Affiliated: No

Abstract

In this research, we define an essential identity for differentiable functions in the framework of tempered fractional integral. By utilizing this identity, we deduce several modifications of fractional Milne-type inequalities. We provide novel expansions of Milne-type inequalities in the domain of tempered fractional integrals. The investigation emphasises important functional categories, including convex functions, bounded functions, Lipschitzian functions, and functions with bounded variation.