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The sequential Henstock-Kurzweil delta integral on time scales

2024; De Gruyter Open; Volume: 57; Issue: 1 Linguagem: Inglês

10.1515/dema-2024-0056

2391-4661

Yang Liu, Yabin Shao,

Fractional Differential Equations Solutions

Abstract 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.