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<p>Based on a topological dual space of an infinite dimensional test space of holomorphic functions, the purpose of this work is to investigate the Wick calculus in white noise theory to introduce the Wick Mittag-Leffler function and the Wick positivity. Using the Riemann–Liouville fractional derivative, the solution of the fractional linear differential equation is given in terms of the Wick Mittag-Leffler function. This solution and the Wick Mittag-Leffler function are shown to be Wick positive.</p>

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Wick Mittag-Leffler function and Wick positivity

  • 期刊论文

  • 发表日期：

    2026年3月16日

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  • Hafedh Rguigui

摘要

Based on a topological dual space of an infinite dimensional test space of holomorphic functions, the purpose of this work is to investigate the Wick calculus in white noise theory to introduce the Wick Mittag-Leffler function and the Wick positivity. Using the Riemann–Liouville fractional derivative, the solution of the fractional linear differential equation is given in terms of the Wick Mittag-Leffler function. This solution and the Wick Mittag-Leffler function are shown to be Wick positive.