On the Analysis of Regularized Fuzzy Systems of Uncertain Differential Equations.

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

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Article in Entropy (Basel, Switzerland), 2023. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Not yet cited in PubMed.

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4 authors.

Anatoliy MartynyukS. P. Timoshenko Institute of Mechanics, NAS of Ukraine, 3 Nesterov Str., 03057 Kiev, Ukraine.

Gani StamovDepartment of Mathematics, University of Texas at San Antonio, San Antonio, TX 78249, USA.

Ivanka StamovaDepartment of Mathematics, University of Texas at San Antonio, San Antonio, TX 78249, USA.ORCID 0000-0001-6723-2699

Yulya Martynyuk-ChernienkoS. P. Timoshenko Institute of Mechanics, NAS of Ukraine, 3 Nesterov Str., 03057 Kiev, Ukraine.

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6 · The paper itself

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.

Indexed as

approximate solutionsautonomous fuzzy differential equationscontinuityfuzzy differential equationsglobal solutionsregularization correctnessstability analysissuccessive approximation

Identifiers

PMID37509956

DOI10.3390/e25071010

PMCPMC10378660

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