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<p>This paper introduces and studies a generalized fractional Clairaut differential equation (<Emphasis FontCategory="NonProportional">GFCDE</Emphasis>) within the framework of Wick calculus over spaces of generalized functions. As a foundational step, we extend the modified Mittag-Leffler function to act on generalized functions. Using this extension, we establish that the explicit solution of the Atangana–Baleanu Caputo (ABC) <Emphasis FontCategory="NonProportional">GFCDE</Emphasis> is given by the Wick product of the initial condition and a fundamental solution, where the latter is formulated as a generalized process involving the modified Mittag-Leffler function. Finally, we demonstrate that the solution admits an integral representation, characterized by a unique positive Radon measure.</p>

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Generalized fractional Clairaut equation in infinite-dimensional spaces

  • 期刊论文

  • 发表日期：

    2026年4月27日

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  • Amine Ettaieb,
  • Hafedh Rguigui

摘要

This paper introduces and studies a generalized fractional Clairaut differential equation (GFCDE) within the framework of Wick calculus over spaces of generalized functions. As a foundational step, we extend the modified Mittag-Leffler function to act on generalized functions. Using this extension, we establish that the explicit solution of the Atangana–Baleanu Caputo (ABC) GFCDE is given by the Wick product of the initial condition and a fundamental solution, where the latter is formulated as a generalized process involving the modified Mittag-Leffler function. Finally, we demonstrate that the solution admits an integral representation, characterized by a unique positive Radon measure.