The cauchy problem for fuzzy differential equations

Fuzzy fractional integral equations under compactness type condition

“…From Theorem 2.1 of [20], we know that E n can be embedded as a closed convex cone in a Banach space X. The embedding map j(·) : E n → X is an isometry and an isomorphism .…”

The Cauchy problems for discontinuous fuzzy systems under generalized differentiability

“…In [24], the author has proved the Cauchy problem has a uniqueness result if f was continuous and bounded. In [16,17], the authors presented a uniqueness result when f satisfies a Lipschitz condition. Because the metric space (E n , D) has a linear structure, it can be imbedded isomorphically as a cone in a Banach space.…”

“…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.…”

Fourth Order Runge-Kutta Method Based On Geometric Mean for Hybrid Fuzzy Initial Value Problems

“…The existence of solutions of fuzzy differential equations has been studied by several authors [3,4]. It is difficult to obtain an exact solution for fuzzy differential equations and hence several numerical methods where proposed [11,12,14,18]. Abbasbandy and Allahviranloo [2] developed numerical algorithms for solving fuzzy differential equations based on Seikkala"s derivative of fuzzy process [25].…”