Fuzzy differential equations and the extension principle
2007
We study the Cauchy problem for differential equations, considering its parameters and/or initial conditions given by fuzzy sets. These fuzzy differential equations are approached in two different ways: (a) by using a family of differential inclusions; and (b) the Zadeh extension principle for the solution of the model. We conclude that the solutions of the Cauchy problem obtained by both are the same. We also provide some illustrative examples.
Keywords:
- Stochastic partial differential equation
- Examples of differential equations
- Differential algebraic equation
- Mathematical optimization
- Mathematics
- Cauchy problem
- Numerical partial differential equations
- Differential algebraic geometry
- Separable partial differential equation
- Hyperbolic partial differential equation
- Mathematical analysis
- Elliptic partial differential equation
- Integrating factor
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