Global existence and uniqueness of solutions for fuzzy differential equations under dissipative-type conditions

Global existence of solutions for fuzzy second-order differential equations under generalized H-differentiability

“…Wu and Gong defined and discussed the (FH) integral for fuzzy number valued functions in [6]. Gong and Shao studied the global existence, uniqueness and the continuous dependence of a solution on fuzzy differential equations under the dissipative-type conditions using the properties of a differential and integral calculus for fuzzy set valued mappings and completeness of metric space of fuzzy numbers in [7]. Park et al proved the existence of solutions to fuzzy integral equations in Banach spaces on [t 0 , t 0 + d] in [8].…”

Numerical Bounded Solutions of Fuzzy Volterra Integral Equations

“…In the paper [20], Jong Yeoul Park proves the existence and uniqueness theorem of a solution to the fuzzy Volterra integral equation. Using the properties of a differential and integral calculus for fuzzy set valued mappings and completeness of metric space of fuzzy numbers, the global existence, uniqueness and the continuous dependence of a solution on a fuzzy differential equation are derived under the dissipative-type conditions [11]. D. N. Georgiou studied fuzzy Volterra integral equation under which the solutions of a fuzzy integral equation are bounded [10].…”

The Cauchy problems for discontinuous fuzzy systems under generalized differentiability

“…The Cauchy problems for fuzzy differential equations have been studied by several authors [12,16,17,24,25,27] on the metric space (E n , D) of normal fuzzy convex set with the distance D given by the maximum of the Hausdorff distance between the corresponding level sets. In [24], the author has proved the Cauchy problem has a uniqueness result if f was continuous and bounded.…”