In this work, we have used fuzzy homotopy analysis method to find the fuzzy series solution (fuzzy semi-analytical solution) of the first order fuzzy Riccati differential equation. The fuzzy approximate-analytical solutions that we obtained during this paper are accurate solutions and very close to the fuzzy exact-analytical solutions. Some numerical results are given to illustrate the method. The obtained numerical results are compared with the exact solutions.
In this work, we have used fuzzy Adomian decomposition method to find the fuzzy semi analytical solution of the fuzzy autonomous differential equations with fuzzy initial conditions. This method allows for the solution of the fuzzy initial value problems to be calculated in the form of an infinite fuzzy series in which the fuzzy components can be easily calculated. The fuzzy series solutions that we have obtained are accurate solutions and very close to the fuzzy exact analytical solutions. Some numerical results have been given to illustrate the efficiency of the used method.
The aim of this work is to present a novel approach based on the artificial neural network for finding the numerical solution of first order fuzzy differential equations under generalized H-derivation. The differentiability concept used in this paper is the generalized differentiability since a fuzzy differential equation under this differentiability can have two solutions. The fuzzy trial solution of fuzzy initial value problem is written as a sum of two parts. The first part satisfies the fuzzy condition, it contains no adjustable parameters. The second part involves feed-forward neural networks containing adjustable parameters. Under some conditions the proposed method provides numerical solutions with high accuracy.
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