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<p>Multivariate uncertain calculus is a branch of mathematics that deals with differentiation and integration of uncertain fields based on uncertainty theory. This paper revises the definition of first partial derivatives of uncertain field and defines higher-order partial derivatives for the first time. Then some sufficient and necessary conditions for uncertain fields possessing partial derivatives are derived. Finally, some examples are documented to verify the solution of higher-order uncertain partial differential equation.</p>

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Higher-order partial derivatives of uncertain field with application to higher-order uncertain partial differential equation

  • 期刊论文

  • 发表日期：

    2025年5月17日

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  • Binhao He,
  • Baoding Liu

摘要

Multivariate uncertain calculus is a branch of mathematics that deals with differentiation and integration of uncertain fields based on uncertainty theory. This paper revises the definition of first partial derivatives of uncertain field and defines higher-order partial derivatives for the first time. Then some sufficient and necessary conditions for uncertain fields possessing partial derivatives are derived. Finally, some examples are documented to verify the solution of higher-order uncertain partial differential equation.