The HK Transform: A Laplace-Based Method for Population Growth and Decay Models
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HK Transform, Inverse HK Transform, Growth Problem, Decay Problem
Abstract
This study examines the use of the HK transform in classical problems in population dynamics, particularly growth and decay processes. Theoretical sociology, applied chemistry, quantitative biology, physical sciences, and financial modelling are among the many disciplines in which these problems are highly relevant. The main aim of this study is to present a range of real-world case studies and to evaluate the effectiveness and accuracy of the HK transform as a reliable analytical tool for solving these differential equations. These examples are selected to demonstrate the transform’s theoretical significance as well as its practical applications across several fields. The study offers a reliable and often simpler alternative to traditional techniques by using the HK transform. The results suggest improved efficiency and reliability in modelling these problems accurately. Overall, this study indicates that the HK transform is a useful tool for researchers studying rates of change in dynamic systems.
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