Existence and uniqueness of approximate solutions to Cauchy problem of complex fuzzy differential equations

Article type: Research Article

Authors: Rashid, Maliha^a | Mehmood, Nayyar^{a; b; *} | Shaheen, Sumbal^a

Affiliations: [a] Department of Mathematics and Statistics, International Islamic University, Islamabad, Pakistan | [b] Department of Mathematical Sciences, College of Science, UAE University, UAE

Correspondence: [*] Corresponding author. Nayyar Mehmood. E-mail: nayyar.mehmood@iiu.edu.pk.

Abstract: In this article we establish a relation between the solutions of complex fuzzy differential equations, with complex membership grades, and approximate solutions by applying the properties of level-wise continuity for (ς, ϑ)-level sets. The notion of H-differentiability is generalized for (ς, ϑ)-level sets in the space Eˆ2n. Results about the existence and uniqueness of the solutions of Cauchy problem for complex fuzzy differential equations are also included.

Keywords: Complex fuzzy differential equations, existence and uniqueness, approximate solutions, level-wise continuity, H-differentiability

DOI: 10.3233/JIFS-181611

Journal: Journal of Intelligent & Fuzzy Systems, vol. 36, no. 4, pp. 3567-3577, 2019