Three Kinds Of Methods For Solving Boundary Value Problems Of Fuzzy Differential Equations

The fuzzy differential equation is an important part of fuzzy mathematics and its solving methods have wide applications in practice. In this paper, three methods for solving boundary value problems of fuzzy differential equations are discussed. We also extend and improve some recent results in the literatures. The paper divided into six chapters. Conclusion is given in chapter 6.The main contents of five chapters are as follows:In the first chapter,we sketch the present situations and the main methods for our investigating problems.In the second chapter,we list some preliminaries which will be used in this paper.In the third chapter, the following boundary value problem of fuzzy differential equation is considered:x"(t)+mx'(t)+nx(t)=f(t),x(a)=b,x(T)=c.By using the strongly generalized differentiability concept the fuzzy Laplace transform formula is extended. Basing on the inverse transformation and the properties of convolution, a transformational solution method for fuzzy differential equations is given.In the fourth chapter, we consider the following second order liner differential equation x"(t) = f(t,x(t)),x(t0) = x0,x(t1) = x1.By using the relationship between the depict equation of fuzzy differential equation and boundary value, the solution of fuzzy differential equation with boundary value conditions concerning triangular fuzzy number is studied.In the fifth chapter, the following third order fuzzy differential equations with fuzzy boundary value is considered:x'"+a1 (t)x" + a2 (t)x' + a3 (t)x = f (t),x(0) = A, x(r)=B, x(T) = C(0?r?T).By using some properties for linear transformation and separating the fuzzy boundary value, a solution method of fuzzy boundary value problem for third-order fuzzy differential equations is given.