The fuzzy Henstock-Kurzweil delta integral on time scales

TL;DR

This paper explores the properties of the fuzzy Henstock-Kurzweil delta integral on time scales, establishing integrability conditions, introducing uniform integrability, and proving key convergence theorems.

Contribution

It introduces the concept of uniform FHK Δ-integrability and provides necessary and sufficient conditions for FHK Δ-integrability on time scales.

Findings

Characterization of FHK Δ-integrability conditions

Introduction of uniform FHK Δ-integrability

Proven monotone and dominated convergence theorems

Abstract

We investigate properties of the fuzzy Henstock-Kurzweil delta integral (shortly, FHK $\Delta$-integral) on time scales, and obtain two necessary and sufficient conditions for FHK $\Delta$-integrability. The concept of uniformly FHK $\Delta$-integrability is introduced. Under this concept, we obtain a uniformly integrability convergence theorem. Finally, we prove monotone and dominated convergence theorems for the FHK $\Delta$-integral.