A Distributional Approach to the Henstock-Kurzweil $\Delta$-Integral on Time Scales

Abstract

In this paper, we explore distribution theory within the framework of time scales. We present several convergence theorems concerning distributions and extend the theory to formulate distributional Henstock-Kurzweil delta integrals-an advancement over standard delta integrals. Fundamental analytical tools such as integration by parts and the Hake theorem are established. We conclude with a discussion of the fundamental theorem for functions integrable in the distributional Henstock-Kurzweil sense over time scales.