Existence and Uniqueness of Solution of Volterra Integral Equations
Abstract
The fuzzy differential and integral equations are important part of the fuzzy analysis theory and they have the important value of theory and application in control theory. Seikkala in [8] has defined the fuzzy derivative which is the generalization of the Hukuhara derivative in [7], the fuzzy integral which is the same as that of Dubois and prade [1], and by means of the extension principle of Zadeh, showed that the fuzzy initial value problem x′(t) = f(t, x(t)), x(0) = x0 has a unique fuzzy solution when f satisfies the generalized Lipschitz condition which guarantees a unique solution of the deterministic initial value problem.Kaleva [3] studied the Cauchy problem of fuzzy differential equation, characterized those subsets of fuzzy sets in which the peano theorem is valid.Park et al. in [5] have considered the existence of solution of fuzzy integral equation in Banach space and Subrahmaniam and Sudarsanam in [9] have proved the existence of solution of fuzzy functional equations.