Solution of fuzzy differential equations

Hybrid system is a dynamic system that exhibits both continuous and discrete dynamic behavior. The hybrid differential equations have a wide range of applications in science and engineering. The hybrid systems are devoted to modeling, design, and validation of interactive systems of computer programs and continuous systems. Hybrid fuzzy differential equations (HFDEs) is considered by Kim et al. [11]. In the present paper it is shown that the example presented by Kim et al. in the Case I is not very accurate and in the Case II, is incorrect. Namely, the exact solution proposed by the authors in the Case II are not solutions of the given HFDE. The correct exact solution is also presented here, together with some results for characterizing solutions of FDEs under Hukuhara differentiability by an equivalent system of ODEs. Then, the homotopy analysis method (HAM) is applied to obtained the series solution of the HFDEs. Finally, we illustrate our approach by a numerical example.

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