Existence, uniqueness and stability of fuzzy delay differential equations with local Lipschitz and linear growth conditions

Document Type : Research Article


1 University of Applied Science and Technology, Center of Poolad Peechkar, Varamin, Iran

2 Department of Applied Mathematics, School of Mathematical Sciences, Ferdowsi University Of Mashhad, Mashhad, Iran

3 Department of Mathematics, Varamin-Pishva Branch, Islamic Azad University, Varamin, Iran

4 Department of Mathematics, Shahr-e-Qods Branch, Islamic Azad University, Tehran, Iran


Fuzzy delay differential equation driven by Liu's process is a type of functional differential equations. In this paper, we are going to provide and prove a novel existence and uniqueness theorem for the solutions of fuzzy delay differential equation under Local Lipschitz and linear growth conditions. Also the stability of the solutions for fuzzy delay differential is investigated. Finally, to illustrate the main results we give some examples.