On fuzzy solutions for heat equation based on generalized Hukuhara differentiability

In this paper a fuzzy heat equation with fuzzy initial values is considered. The concept of generalized Hukuhara differentiation is interpreted thoroughly in the univariate and multivariate cases, and also several properties for generalized Hukuhara differentiability are obtained on the topics, such as switching point, the univariate and multivariate fuzzy chain rules, fuzzy mean value theorem, among others. The objective of this paper is to prove the uniqueness of a solution for a fuzzy heat equation and show that a fuzzy heat equation can be modeled as two systems of fuzzy differential equations by considering the type of differentiability of solutions. Finally, some examples show the behavior of the solutions obtained.