About the Existence and Uniqueness Theorem of Fuzzy Random Ordinary Differential Equations

Authors

  • Osama M. Atyia Ph.D. Student, Department of Mathematics, College of Computer Science and Mathematics, Tikrit University, Tikrit, Iraq
  • Fadhel S. Fadhel Department of Mathematics and Computer Applications, College of Science, Al-Nahrain University, Jadriya, Baghdad, Iraq
  • Mizal H. Alobaidi Department of Mathematics, College of Computer Science and Mathematics, Tikrit University, Tikrit, Iraq

Keywords:

Banach contraction mapping theorem, Generalized contraction, Lipschitz condition, Fuzzy random ordinary differential equations, Stochastic process

Abstract

    Ordinary differential equations that includes stochastic processes in their vector fields are called random ordinary differential equations, that are considered through this work as a Weiner process or also called Brownian motion. In this paper, fuzzy random ordinary differential equations are considered, in which the fuzziness appears in the initial conditions in terms of triangular fuzzy numbers. Such equations are crucial in the theory of random dynamical systems and/or modern control theory and therefore the existence of a unique solution of such equations is of great importance. The statement and the proof of the existence and uniqueness theorem of fuzzy random ordinary differential equations is the main objective of this paper, which is proved using Banach contraction mapping theorem.

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Published

2023-07-01

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Section

Articles

How to Cite

(1)
About the Existence and Uniqueness Theorem of Fuzzy Random Ordinary Differential Equations. ANJS 2023, 26 (2), 30-35.