On Darboux-Type Differential Inclusions with Uncertainty

Abstract

In this article we prove the existence results for solutions of the Darboux-type problems in fuzzy partial differential inclusions with local conditions of integral types. We present two problems involving open and closed level sets of a given fuzzy mapping. In the first case fuzzy differential inclusion has been transformed into an equivalent Darboux-type problem for partial differential equations and then using the Tychonoff fixed point theorem we prove the existence result for this crisp case. For the second case we use Nadler’s fixed point theorem and selection theorem of Kuratowski-Ryll-Nardzewski to find the solution of given differential inclusions problem. We furnish an example to validate our results.