Generalized H-differentiability for solving second order linear fuzzy differential equations

In this paper, a new approach for solving the second order fuzzy differential equations (fde) with fuzzy initial value, under strongly generalized h-differentiability is presented. solving first order fuzzy differential equations by extending 1-cut solution of the original problem and solving fuzzy integrodifferential equations has been investigated by some authors (see for example [5, 6]), but these methods have been done for fuzzy problems with triangular fuzzy initial value. therefore by extending the r-cut solutions of the original problem we will obviate this deficiency. the presented idea is based on: if a second order fuzzy differential equation satisfy the lipschitz condition then the initial value problem has a unique solution on a specific interval, therefore our main purpose is to present a method to find an interval on which the solution is valid