In this paper, the multiple solutions of Nth-order fuzzy differential equations by the equivalent integral forms are considered. Also, an Existence and uniqueness theorem of solution of Nth-order fuzzy differential equations is proved under Nth-order generalized differentiability in Banach space.

In this paper, we study the numerical method for Nonlinear Fuzzy Differential Equations by an application of the Leapfrog method for fuzzy differential equations. And, we present an example with initial condition [28] having two different solutions to illustrate the efficiency of the proposed Leapfrog method. Solution graphs are presented to highlight the efficiency of the Leapfrog method.

Existence and uniqueness theorems are proved for Cauchy problems of second-order fuzzy differential equations. 1. Introduction. In 1972, Chang and Zadeh [2] first introduced the concept of fuzzy derivative, followed up ten years later by Dubois and Prade [5], who used the extension principle in their approach. In the mean time, Puri and Ralescu [12] used the notion of H-differentiability to ext...

Abstract Chebyshev collocation scheme and Finite difference method plays central roles for solving fractional differential equations (FDE). Therefore purpose of this paper is to solve mathematical problem diffusion by which turns the original problems into system ordinary algebraic imposing orthogonality property. This solved implementing method. The numerical illustrations confirm that combina...

The fuzzy differential and integral equations are important part of the fuzzy analysis theory. Park et al. [8] have considered the existence of solution of fuzzy integral equation in Banach space and Subrahmaniam and Sudarsanam [12] proved the existence of solution of fuzzy functional equations. An integral equation is called singular if either the range of integration is infinite or the kernel...

In this paper, we study first order linear fuzzy differential equations with fuzzy coefficient and initial value. We use the generalized differentiability concept and apply the exponent matrix to present the general form of their solutions. Finally, one example is given to illustrate our results.

In this paper, fuzzy variational iteration method (FVIM) is proposed to solve the second- order fuzzy Abel-Volterra integro-differential equations. The existence and uniqueness of the solution and convergence of the proposed method are proved in details. is investigated to verify convergence results and to illustrate the efficiently of the method.

In this research, we employ a newly developed strategy based on modified version of the Adomian decomposition method (ADM) to solve nonlinear fractional differential equations (FDE) with both and nondifferential variables. FDE have disturbed interest many researchers. This is due development theory applications calculus. track from various areas can be used model fields science engineering such...

We study the Cauchy problem for differential equations, considering its parameters and/or initial conditions given by fuzzy sets. These fuzzy differential equations are approached in two different ways: (a) by using a family of differential inclusions; and (b) the Zadeh extension principle for the solution of the model. We conclude that the solutions of the Cauchy problem obtained by both are t...