Two point fuzzy boundary value problem with eigenvalue parameter contained in the boundary condition

Abstract

In this article two point fuzzy boundary value problem is defined under the approach generalized Hukuhara differentiability ( $\mathrm{gH}$-differentiability). We research the solution method of the fuzzy boundary problem with the basic solutions $\Phi(x, \lambda)$ and $\widehat{\chi}(x, \lambda)$ which are defined by the special procuder. We give operator-theoretical formulation, construct fundamental solutions and investigate some properties of the eigenvalues and corresponding eigenfunctions of the considered fuzzy problem. Then results of the proposed method are illustrated with a numerical example.