Existence and Uniqueness of Solutions of Implicit Fuzzy Differential Equations
In this paper,we study the existence and uniqueness of solutions for the following implicit fuzzy differential equation initial value problem and boundary value problem.{x'(t)=f(t,x(t),x'(t)),t ∈[0,T]x(0)=x0,x0 ∈ E and {x'(t)=f(t,x(t),x'(t))x(0)=λx(T),x(0)∈ E Based on the strong generalized differential,the integral equivalent form of implicit fuzzy differential equation is given,and the existence and uniqueness of the solution is proved by using the principle of generalized contractive mapping.Finally,a specific example is given to verify its rationality.
generalized differentiabilityfuzzy differential equationsinitial value problemboundary value problem
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