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

Subject Areas : International Journal of Industrial Mathematics

P. Darabi ¹ , S. Moloudzadeh‎ ² , H. Khandani‎ ³

1 - Department of Mathematics, Farhangian University, Tehran, Iran.
2 - Department of Mathematics, Faculty of Education, Soran University, Soran/Erbil, Kurdistan Region, Iraq.
3 - Department of Mathematics, Mahabad Branch, Islamic Azad University, Mahabad, Iran.

Received: 2016-08-28 Accepted : 2016-08-28 Published : 2016-08-01

Keywords: Fuzzy differential equations (, Strongly generalized H-differe, r-cut ‎solutions,

Abstract :

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 integro-differential equations has been investigated by some authors (see for example \cite{darabi1,TS}), 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.