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