## Abstract

Uncertain nonlinear systems can be modeled with fuzzy differential equations (FDEs) and the solutions of these equations are applied to analyze many engineering problems. However, it is very difficult to obtain solutions of FDEs.

In this book chapter, the solutions of FDEs are approximated by utilizing the fuzzy Sumudu transform (FST) method. Here, the uncertainties are in the sense of fuzzy numbers and Z-numbers. Important theorems are laid down to illustrate the properties of FST. This new technique is compared with Average Euler method and Max-Min Euler method. The theoretical analysis and simulation results show that the FST method is effective in estimating the solutions of FDEs.

In this book chapter, the solutions of FDEs are approximated by utilizing the fuzzy Sumudu transform (FST) method. Here, the uncertainties are in the sense of fuzzy numbers and Z-numbers. Important theorems are laid down to illustrate the properties of FST. This new technique is compared with Average Euler method and Max-Min Euler method. The theoretical analysis and simulation results show that the FST method is effective in estimating the solutions of FDEs.

Original language | English |
---|---|

Title of host publication | Advanced Fuzzy Logic Approaches in Engineering Science |

Editors | Mangey Ram |

Publisher | IGI Global |

Chapter | 2 |

Pages | 18-48 |

Number of pages | 31 |

ISBN (Electronic) | 9781522557104 |

ISBN (Print) | 9781522557098 |

DOIs | |

Publication status | Published - 1 Sept 2018 |

## Keywords

- Fuzzy Sumudu transform
- Fuzzy differential equations
- Modeling
- Approximate solution
- Z-numbers
- Fuzzy numbers
- Euler method
- Uncertain nonlinear systems
- Max-Min Euler