Analytical and numerical solution of differential equations with generalized fuzzy derivative

Abstract

The aim of this work is to present a novel approach based on the fuzzy neural network for finding the numerical solution of the first order fuzzy differential equations under generalized H-derivation .The differentiability concept that used in this paper is the generalized differentiability since a first order fuzzy differential equation under this differentiability can have two solutions .The fuzzy trial solution of the fuzzy initial value problem is written as a sum of two parts. The first part satisfies the fuzzy condition, it contains no fuzzy adjustable parameters. The second part involves fuzzy feed-forward neural networks containing fuzzy adjustable parameters. This method, in comparison with existing numerical methods and the analytical solutions, shows that the use of fuzzy neural networks provides solutions with good generalization and high accuracy.