Stability of Uncertain Equations of Volterra-Levin type and an Uncertain Delay Differential Equation Via Fixed Point Method‎

Stability of Uncertain Equations of Volterra-Levin type and an Uncertain Delay Differential Equation Via Fixed Point Method‎

Authors

  • Vahid ROOMİ*, Hamid Reza AHMADİ

Keywords:

Stability, Lyapunov, Fixed point techniques, Uncertain delay differential equations

Abstract

‎In this work four uncertain delay differential equations of Volterra-Levin type will be considered‎. ‎Applying suitable contraction mapping and fixed point method‎, ‎the stability of the equations will be studied‎. ‎It will be shown that the solutions are bounded and‎, ‎with additional condition‎, ‎the solutions tend to zero‎. ‎Also‎, ‎a necessary and sufficient condition for the asymptotic stability of the solutions of an uncertain differential equation will be presented‎.

References

X. Chen, B. Liu, Existence and uniqueness theorem for uncertain differential equations. Fuzzy Optimization and Decision Making 9(1), 69–81 (2010).

X. Ji, J. Zhou, Multi-dimensional uncertain differential equation: Existence and uniqueness of solution. Fuzzy Optimization and Decision Making 14(4), 477–491 (2015).

B. Liu, Some research problems in uncertainty theory. Journal of Uncertain Systems 3(1), 3-10 (2009).

B. Liu, Theory and Practice of Uncertain Programming, 2nd Edition. Springer-Verlag, Berlin, 2009.

B. Liu, Toward uncertain finance theory. Journal of Uncertainty Analysis and Applications 1, (2013) Article 1.

B. Liu, Uncertain logic for modeling human language. Journal of Uncertain Systems 5(1), 3–20 (2011).

B. Liu, Uncertain risk analysis and uncertain reliability analysis. Journal of Uncertain Systems 4(3), 163–170 (2010).

B. Liu, Uncertainty Theory, 2nd ed. Springer-Verlag, Berlin, (2007).

V. Roomi, H. Ahmadi, Continuity and Differentiability of Solutions with Respect to Initial Conditions and Peano Theorem for Uncertain Differential Equations. Mathematics Interdisciplinary Research 7, 249-260 (2022).

V. Roomi, H. Ahmadi, Existence and uniqueness of solutions of uncertain linear systems. Computation Methods for Differential Equations 9(1), 289–299 (2021).

V. Roomi, H. Ahmadi, The Liouville formula and explicit solutions of uncertain homogeneous linear systems. Differential Equations and Dynamical Systems, https://doi.org/10.1007/s12591-021-00573-9.

A. Salim, S. Abbas, M. Benchohra, E. Karapinar, Global stability results for VolterraHadamard random partial fractional integral equations. Rendiconti del Circolo Matematico di Palermo Series 2, (2022). https://doi.org/10.1007/s12215-022-00770-7

X. Yang, J. Gao, Linear-quadratic uncertain differential game with application to resource extraction problem. IEEE Transactions on Fuzzy Systems 24(4), 819–826 (2015).

X.F. Yang, K. Yao, Uncertain partial differential equation with application to heat conduction. Fuzzy Optimization and Decision Making 16(3), 379–403 (2017).

K. Yao, J. Gao, Y. Gao, Some stability theorems of uncertain differential equation. Fuzzy Optimization and Decision Making 12(1), 3–13 (2013).

Y. Zhu, Uncertain optimal control with application to a portfolio selection model. Cybernetics and Systems 41(7), 535–547 (2010)

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Published

2023-08-01

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Articles

How to Cite

Stability of Uncertain Equations of Volterra-Levin type and an Uncertain Delay Differential Equation Via Fixed Point Method‎ . (2023). Advances in the Theory of Nonlinear Analysis and Its Application, 7(1), 215-231. https://atnaea.org/index.php/journal/article/view/42