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<p>In this paper, we introduce a new Laplace transform of a positive measure on a time scale. The proposed Laplace transform generalizes the classical one in the context of time scales. First, we adapt several classical results related to positive measures in the context of time scales. These technical propositions are used to establish the convexity of the proposed new time scale Laplace transform. Moreover, we show that this new transform characterizes the measure. Finally, we compute the transform for several probability distributions that have been previously defined directly on time scales (Bernoulli, binomial, Poisson, exponential), thereby illustrating its relevance in the time scales probability setting.</p>

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A NEW LAPLACE TRANSFORM OF A POSITIVE MEASURE ON TIME SCALES

  • 期刊论文

  • 发表日期：

    2026年7月2日

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  • Aljia Nouha Ben Afia,
  • Abdelaziz Ghribi,
  • Khalil Masmoudi

摘要

In this paper, we introduce a new Laplace transform of a positive measure on a time scale. The proposed Laplace transform generalizes the classical one in the context of time scales. First, we adapt several classical results related to positive measures in the context of time scales. These technical propositions are used to establish the convexity of the proposed new time scale Laplace transform. Moreover, we show that this new transform characterizes the measure. Finally, we compute the transform for several probability distributions that have been previously defined directly on time scales (Bernoulli, binomial, Poisson, exponential), thereby illustrating its relevance in the time scales probability setting.