Uniqueness and Existence of Solutions of the Periodic First-Order Fuzzy Differential Equation with Boundary Value Using Fixed Point Theorems
نویسندگان
چکیده
The theory of fuzzy functions and its application has increased recently due to the industrial interest of fuzzy control. Moreover, in view of the development of the calculus for fuzzy functions, the investigation of fuzzy differential equations has been initiated and the existence and uniqueness of solutions of fuzzy initial value problem was considered under a Lipschitz condition (Kaleva, 1987; Kaleva, 1990). The basic result such as existence, uniqueness, continuity with respect to initial values and global existence, are proved by developing the needed general comparison principle which helps to understand the intricacies involved in incorporating fuzziness in differential equations (Lakshmikantham,). Seikkala (1987) proved the existence and uniqueness of the fuzzy solution for the following systems:
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