Existence and uniqueness of mild solution for initial value problem of a class of fuzzy evolution equations with delay

Document Type : Research Paper

Author

Northwest normal University, Anning District, Lanzhou City, Gansu Province

Abstract

In this paper, we consider a class of fuzzy delay evolution equations under generalized differentiability. By using the operator semigroup theory, the upper and lower solutions and the monotone
iterative technique, the existence and uniqueness of mild solutions for the initial value problem of fuzzy
delay evolution equations are obtained. The continuous dependence of two kinds of mild solutions on
the initial value is also proved. In particular, the first innovation of this paper is to introduce the delay
term into the fuzzy evolution equation, and the second innovation is that when discussing the continuous
dependence of the solution on the initial value, it completely eliminates the restriction of the nonlinear
function on the Lipschitz condition coefficients and optimizes the conditions for the existence of the solutions, which is relatively rare. Corresponding examples are added at the end of the article to make the
conclusion better applied to practice.

Keywords

Main Subjects

References

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Iranian Journal of Fuzzy Systems
Volume 22, Issue 6
November and December 2025
Pages 67-81

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