EXISTENCE AND UNIQUENESS THEOREM FOR A SOLUTION OF FUZZY DIFFERENTIAL EQUATIONS
By using the method of successive approximation, we prove the existence and uniqueness of a solution of the fuzzy differential equation x'(t) = f(t, x(t)), x(t_0) = x_0. We also consider an ∈-approximate solution of the above fuzzy differential equation.
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| Published in | International Journal of Mathematics and Mathematical Sciences Vol. 1999; no. 2; pp. 271 - 279 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Hindawi Limiteds
01.01.1999
Wiley |
| Subjects | |
| Online Access | Get full text |
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| Abstract | By using the method of successive approximation, we prove the existence and uniqueness of a solution of the fuzzy differential equation x'(t) = f(t, x(t)), x(t_0) = x_0. We also consider an ∈-approximate solution of the above fuzzy differential equation. |
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| AbstractList | By using the method of successive approximation, we prove the existence and uniqueness of a solution of the fuzzy differential equation x′(t)=f(t,x(t)),x(t0)=x0. We also consider an ϵ-approximate solution of the above fuzzy differential equation. By using the method of successive approximation, we prove the existence and uniqueness of a solution of the fuzzy differential equation x(t)=f(t,x(t)),x(t0)=x0. We also consider an -approximate solution of the above fuzzy differential equation. By using the method of successive approximation, we prove the existence and uniqueness of a solution of the fuzzy differential equation x ′ ( t ) = f ( t , x ( t )), x ( t 0 ) = x 0 . We also consider an ϵ ‐approximate solution of the above fuzzy differential equation. By using the method of successive approximation, we prove the existence and uniqueness of a solution of the fuzzy differential equation x'(t) = f(t, x(t)), x(t_0) = x_0. We also consider an ∈-approximate solution of the above fuzzy differential equation. |
| Author | JONG YEOUL PARK HYO KEUN HAN |
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| Keywords | levelwise continuous fuzzy differential equation fuzzy integral fuzzy solution fuzzy derivative Fuzzy set-valued mapping fuzzy ∈-approximate solution |
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| Snippet | By using the method of successive approximation, we prove the existence and uniqueness of a solution of the fuzzy differential equation x'(t) = f(t, x(t)),... By using the method of successive approximation, we prove the existence and uniqueness of a solution of the fuzzy differential equation x ′ ( t ) = f ( t , x (... By using the method of successive approximation, we prove the existence and uniqueness of a solution of the fuzzy differential equation... |
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| StartPage | 271 |
| SubjectTerms | fuzzy derivative fuzzy differential equation fuzzy integral Fuzzy set-valued mapping fuzzy solution fuzzy ϵ solution levelwise continuous |
| Title | EXISTENCE AND UNIQUENESS THEOREM FOR A SOLUTION OF FUZZY DIFFERENTIAL EQUATIONS |
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