Series Solution of the System of Fuzzy Differential Equations

Abstract

The homotopy analysis method (HAM) is proposed to obtain a semianalytical solution of the system of fuzzy differential equations (SFDE). The HAM contains the auxiliary parameterħ, which provides us with a simple way to adjust and control the convergence region of solution series. Concept ofħ-meshes and contour plots firstly are introduced in this paper which are the generations of traditionalh-curves. Convergency of this method for the SFDE has been considered and some examples are given to illustrate the efficiency and power of HAM.

Numerical Solution of Uncertain Beam Equations Using Double Parametric Form of Fuzzy Numbers

“…Here, is considered as a small homotopy parameter 0 ≤ ≤ 1. For = 0, (19) and (20) become a linear equation; that is, 2 V( ; , )/ 2 = 0, which is easy to solve. For = 1, (19) and (20) turn out to be same as the original equation (16).…”

“…Similarly, many authors studied various other methods to solve th order fuzzy differential equations in [17][18][19][20][21]. Based on the idea of collocation method, Allahviranloo et al [17] investigated the numerical solution of th order fuzzy differential equations.…”

“…Parandin [19] discussed Runge-Kutta method for the numerical solution of fuzzy differential equations of thorder. Hashemi et al [20] studied homotopy analysis method for the solution of system of fuzzy differential equations. Zhang and Wang [21] utilized time domain methods for the solutions of th-order fuzzy differential equations.…”

Global exponential stability and existence of periodic solutions of fuzzy wave equations

“…In [3], the authors prove the existence and uniqueness of the solution of the FDEs with the right-hand side satisfying the Lipschitz condition by the concept of Hukuhara derivative. For more examples one can refer to the significant results in [4][5][6][7][8][9][10][11][12][13][14][15][16]. Therefore, the construction of a theory that combines appropriately the theory of impulsive differential equations with that of FDEs is essential.…”

System of Differential Equation with Initial Value as Triangular Intuitionistic Fuzzy Number and its Application

“…Numerical solution of SFDE is developed by Fard [27]. The geometric approach is developed by Gasilova et al in [28] and series solution is developed by Hashemi et al [29]. There are other meny approaches to solve this SFDE (see [30][31][32]).…”