Solution to the Bessel differential equation with interactive fuzzy boundary conditions

Abstract

In this paper we deal with the fuzzy boundary value problem of the Bessel differential equation, whose boundary conditions are uncertain and given by linearly interactive fuzzy numbers. The Bessel differential equation can be considered in order to model wave and heat propagation problems. The fuzzy solution is obtained from the sup-J extension principle. We show that the sup-J extension provides proper fuzzy solution for the Bessel differential equation. In addition, we study the advantages of the proposed approach with others well known methods, such as the solutions based on the Zadeh extension principle and the solutions derived from the generalized Hukuhara derivative.