## Abstract

In this paper, a numerical solution (*Euler* method) for solving first-order fully fuzzy differential equations (*FFDE*) in the form \(y'(t)=a\otimes y(t),~y(0)=y_0,t\in [0,T]\) under strongly generalized H-differentiability is considered. First, we will show that under H-differentiability the *FFDE* can be divided into four differential equations. Then, we will prove that each of divided differential equations satisfies the *Lipschitz* condition, therefore, *FFDE* has a unique solution and *Euler* method can be used to find an approximate solution in each case. Convergence of this method is proved and an algorithm by which the exact solution can be approximated in each case will be provided.

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## Additional information

Communicated by V. Loia.

## Appendices

### Appendix A

*MATLAB* implementation for the *Euler* method to find approximate solutions of *FFDE* (3.1) in case (1):

### Appendix B

*MATLAB* implementation for the *Euler* method to find approximate solutions of *FFDE* (3.1) in case (2):

### Appendix C

*MATLAB* implementation for the *Euler* method to find approximate solutions of *FFDE* (3.1) in case (3):

### Appendix D

*MATLAB* implementation for the *Euler* method to find approximate solutions of *FFDE* (3.1) in case (4):

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Darabi, P., Moloudzadeh, S. & Khandani, H. A numerical method for solving first-order fully fuzzy differential equation under strongly generalized H-differentiability.
*Soft Comput* **20**, 4085–4098 (2016). https://doi.org/10.1007/s00500-015-1743-0

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DOI: https://doi.org/10.1007/s00500-015-1743-0

### Keywords

- Approximate solution
- Cross product
- First-order fully fuzzy differential equation (
*FFDE*) -
*Lipschitz*condition - Strongly generalized H-differentiability