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The sequential Henstock-Kurzweil delta integral on time scales

Liu Yang, Shao Yabin

Demonstratio Mathematica

2024

Vol. 57, nr 1

art. no. 20240056

In this study, the basic theory of the sequential Henstock-Kurzweil delta integral on time scales will be discussed. First, we give the notion and the elementary properties of this integral; then we show the equivalence of the Henstock-Kurzweil delta integral and the sequential Henstock-Kurzweil delta integral on time scales. In addition, we consider the Cauchy criterion and the Fundamental Theorems of Calculus. Finally, we prove Henstock’s lemma and give some convergence theorems. As an application, we consider the existence theorem of a kind of functional dynamic equations.