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Existence and uniqueness of mild solution for initial value problem of a class of fuzzy evolution equations with delay | ||
| Iranian Journal of Fuzzy Systems | ||
| دوره 22، شماره 6، بهمن و اسفند 2025، صفحه 67-81 اصل مقاله (493.93 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2025.49723.8779 | ||
| نویسنده | ||
| Yongwei Jia* | ||
| Northwest normal University, Anning District, Lanzhou City, Gansu Province | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Fuzzy delay evolution equations؛ monotone iterative technique؛ fuzzy strongly continuous semigroup؛ fuzzy mild solution؛ existence and uniqueness | ||
| مراجع | ||
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