Fuzzy Laplace transforms. (English) Zbl 1187.44001
The fuzzy Laplace transform method solves fuzzy differential equations (FDEs) and corresponding fuzzy initial and boundary value problems. Fuzzy Laplace transforms reduce the problem of solving a FDE to an algebraic problem. This switching from operations of calculus to algebraic operations on transforms is called operational calculus, a very important area of applied mathematics, and for the engineer, the fuzzy Laplace transform method is practically the most important operational method. The fuzzy Laplace transform also has the advantage that it solves problems directly, fuzzy initial value problems without first determining a general solution, and non-homogeneous differential equations without first solving the corresponding homogeneous equation.
In this paper, the authors propose a fuzzy Laplace transform and under a strongly generalized differentiability concept, they use it in an analytic solution method for some fuzzy differential equations. The related theorems and properties are proved in detail and the method is illustrated by solving some examples.
In this paper, the authors propose a fuzzy Laplace transform and under a strongly generalized differentiability concept, they use it in an analytic solution method for some fuzzy differential equations. The related theorems and properties are proved in detail and the method is illustrated by solving some examples.
Reviewer: Kun Soo Chang (Seoul)
MSC:
| 44A10 | Laplace transform |
| 34A25 | Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. |
| 34A07 | Fuzzy ordinary differential equations |
Keywords:
fuzzy number; fuzzy Laplace transform; strongly generalized differential; fuzzy differential equation; fuzzy valued function; fuzzy initial and boundary value problems; operational calculus; strongly generalized differentiability conceptReferences:
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