On the Analysis of Regularized Fuzzy Systems of Uncertain Differential Equations

Date

2023-06-30

Authors

Martynyuk, Anatoliy
Stamov, Gani
Stamova, Ivanka
Martynyuk-Chernienko, Yulya

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

This article analyzes a regularized set of fuzzy differential equations with respect to an uncertain parameter. We provide sufficient conditions for the correctness of a new regularization scheme. For the resulting family of regularized fuzzy differential equations, the following properties are analyzed, and efficient criteria are proposed: successive approximations, continuity, global existence of solutions, existence of approximate solutions, existence of solutions in the autonomous case. In addition, we develop stability criteria for the regularized family of fuzzy differential equations on the basis of the comparison technique and the method of nonlinear integral inequalities. We expect that the derived results will inspire future research work in this direction.

Description

Keywords

fuzzy differential equations, regularization correctness, successive approximation, continuity, global solutions, approximate solutions, autonomous fuzzy differential equations, stability analysis

Citation

Entropy 25 (7): 1010 (2023)

Department

Mathematics