Stability of Uncertain Equations of Volterra-Levin type and an Uncertain Delay Differential Equation Via Fixed Point Method‎-Reference-Cited by-同舟云学术

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

Published:2023-03-31 Issue:1 Volume:7 Page:215-231
ISSN:2587-2648
Container-title:Advances in the Theory of Nonlinear Analysis and its Application
language:
Short-container-title:

Author:

ROOMİ Vahid¹^ORCID,AHMADİ Hamid Reza¹^ORCID

Affiliation:

1. Azarbaijan Shahid Madani University

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.

Publisher

Erdal Karapinar

Subject

Applied Mathematics,Analysis

Reference16 articles.

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

2. [2] X. Ji, J. Zhou, Multi-dimensional uncertain differential equation: Existence and uniqueness of solution. Fuzzy Optimization and Decision Making 14(4), 477–491 (2015).

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

4. [4] B. Liu, Theory and Practice of Uncertain Programming, 2nd Edition. Springer-Verlag, Berlin, 2009.

5. [5] B. Liu, Toward uncertain finance theory. Journal of Uncertainty Analysis and Applications 1, (2013) Article 1.