Abstract
The 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 paper, the solutions of FDEs are approximated by utilizing the fuzzy Sumudu transform (FST) method. Significant theorems are suggested in order to explain the properties of FST. The proposed method is validated with three real examples.
Highlights
In many physical and dynamical processes, mathematical modeling leads to the deterministic initial and boundary value problems
In [21], Sumudu transform is suggested in order to solve fuzzy partial differential equations
We extend our previous work [24] by generating more theorems for describing the properties of fuzzy Sumudu transform (FST)
Summary
In many physical and dynamical processes, mathematical modeling leads to the deterministic initial and boundary value problems. If the errors are random, in this case, we have a stochastic differential equation along with the random boundary value. The fuzzy derivative, as well as fuzzy differential equations (FDE), have been discussed in [3,4]. Sumudu transform is popularized in order to solve fractional local differential equations [16,17,18,19,20]. In [21], Sumudu transform is suggested in order to solve fuzzy partial differential equations. In [23] the variational iteration technique is proposed utilizing Sumudu transform for solving ordinary equations. By utilizing the proposed technique, the fuzzy boundary value problem can be resolved directly without determining a general solution. Theorem 2. [29] The FDE is equivalent to a system of ordinary differential equations under generalized differentiability
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