On the existence and uniquness theorem of the global solutions for UFDES

Document Type : Research Paper

Authors

1 University of applied sciences and technology of centre Mahan Hedayat, Iran

2 Department of mathematics, Qazvin branch, Islamic Azad University, Qazvin, Iran.

10.22103/jmmrc.2021.17508.1142

Abstract

The uncertain functional differential equation (UFDE) is a type of functional differential equations driven by a canonical uncertain process. Uncertain functional differential equation with infinite delay (IUFDE) have been widely applied in sciences and technology. In this paper, we prove an existence and uniqueness theorem for IUFDE intheinterval $[t_{0},T]$, underuniform Lipschitz condition and weak condition. Also, the novel existence and uniqueness theorem under the linear growth condition and the local Lipschitz condition is proven. In the following, a more general type of UFDE considers, which the future state is determined by entire of the past states rather than some of them. Finally, the existence and uniqueness theorem is considered on theinterval $[t_{0},\infty ]$.

Keywords


[1] X. Chen, X. Qin. A new existence and uniqueness theorem for fuzzy di erential equations. International Journal of Fuzzy Systems vol., no. 13(2) (2013) 148-151.
[2] Y. Gao. Existence and Uniqueness Theorem on Uncertain Di erential Equations with Local Lipschitz Condition, Journal of Uncertain Systems vol., no. 6(3) (2012) 223-232.
[3] W. Fei. Uniqueness of solutions to fuzzy di erential equations driven by Lius process with non-Lipschitz coecients, Internatinal Confrance On Fuzzy and Knowledge Discovery (2009) 565-569.
[4] Y. Gao. Existence and uniqueness theorem on uncertain di erential equation with local Lipschitz codition, Uncertain Syst., vol., no. 6(3) (2012) 223-232.
[5] B. Liu. Uncertainty Theory, Springer-Verlag. Berlin ( 2004).
[6] K. Yao. A type of uncertain di erential equations with an alytic solution, J. Uncertain. Anal. Appl., vol., no. 8(1) (2013).
[7] Y. Zhu. Uncertain optimal control with application to a portfolio selection model, Cybernet. Syst vol., no. 41(7) (2010) 535-547.