Mild solution for nonlocal impulsive functional fuzzy nonlinear integro-differential equations

• Published in: Fixed point theory and algorithms for sciences and engineering Vol. 2025; no. 1; pp. 12 - 19
• Main Authors: Qumami, Najat H. M., Jain, R. S., Reddy, B. Surendranath
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 19.05.2025; Springer Nature B.V; SpringerOpen
• Subjects: Algorithms; Analysis; Applications of Mathematics; Differential equations; Differential Geometry; Existence theorems; Fixed point theorems; Fixed points (mathematics); Fuzzy sets; Hypotheses; Impulsive functional; Mathematical and Computational Biology; Mathematics; Mathematics and Statistics; Mild solution; Nonlinear fuzzy integro-differential equations; Nonlocal condition; Set theory; Theorems; Topology; Uniqueness theorems; 34A07; 47H10; Nonlinear fuzzy integro-differential equations; 34A12; Impulsive functional; Fixed point theorems; Nonlocal condition; Mild solution
• ISSN: 2730-5422; 2730-5422
• DOI: 10.1186/s13663-024-00779-w

The aim of this paper is to study the existence, uniqueness, and continuous dependence of fuzzy solutions for first-order, nonlocal, impulsive, functional, nonlinear integro-differential equations by using Banach and Krasnoselskii–Schaefer type fixed point theorems. The theorems on the existence and uniqueness of fuzzy solutions for these problems with nonlocal conditions are presented under certain assumptions, and fuzzy theory is the main technique used to establish these results. Finally, an example is given to clarify the effectiveness of this theory.