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2023, Volume 31, Issue 7: 3832-3847. doi: 10.3934/era.2023195
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Regularization scheme for uncertain fuzzy differential equations: Analysis of solutions

  • 1.
    S. P. Timoshenko Institute of Mechanics, NAS of Ukraine, 3 Nesterov str., Kiev-57, 03057, Ukraine
  • 2.
    Department of Mathematics, University of Texas at San Antonio, One UTSA Circle, San Antonio, TX, 78249, USA
  • Received: 02 February 2023 Revised: 21 April 2023 Accepted: 26 April 2023 Published: 11 May 2023

  • In this paper a regularization scheme for a family of uncertain fuzzy systems of differential equations with respect to the uncertain parameters is introduced. Important fundamental properties of the solutions are discussed on the basis of the established technique and new results are proposed. More precisely, existence and uniqueness criteria of solutions of the regularized equations are established. In addition, an estimation is proposed for the distance between two solutions. Our results contribute to the progress in the area of the theory of fuzzy systems of differential equations and extend the existing results to the uncertain case. The proposed results also open the horizon for generalizations including equations with delays and some modifications of the Lyapunov theory. In addition, the opportunities for applications of such results to the design of efficient fuzzy controllers are numerous.

    Citation: Anatoliy Martynyuk, Gani Stamov, Ivanka Stamova, Yulya Martynyuk–Chernienko. Regularization scheme for uncertain fuzzy differential equations: Analysis of solutions[J]. Electronic Research Archive, 2023, 31(7): 3832-3847. doi: 10.3934/era.2023195

    Related Papers:

  • In this paper a regularization scheme for a family of uncertain fuzzy systems of differential equations with respect to the uncertain parameters is introduced. Important fundamental properties of the solutions are discussed on the basis of the established technique and new results are proposed. More precisely, existence and uniqueness criteria of solutions of the regularized equations are established. In addition, an estimation is proposed for the distance between two solutions. Our results contribute to the progress in the area of the theory of fuzzy systems of differential equations and extend the existing results to the uncertain case. The proposed results also open the horizon for generalizations including equations with delays and some modifications of the Lyapunov theory. In addition, the opportunities for applications of such results to the design of efficient fuzzy controllers are numerous.


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