Higher-order derivative of uncertain process and higher-order uncertain differential equation

Kaixi Zhang () and Baoding Liu ()
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Kaixi Zhang: Tsinghua University
Baoding Liu: Tsinghua University

Fuzzy Optimization and Decision Making, 2024, vol. 23, issue 2, No 7, 295-318

Abstract: Abstract This paper initializes higher-order uncertain calculus that deals with higher-order differentiation and multiple integration of uncertain process based on uncertainty theory. Fubini theorem and fundamental theorem of higher-order uncertain calculus are derived. Finally, this paper rigorously defines higher-order uncertain differential equations and introduces some analytic methods for solving these equations.

Keywords: Uncertainty theory; Uncertain calculus; Uncertain differential equation; Higher-order derivative (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10700-024-09422-0

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