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.

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...

This study aims to solve the nonlinear fractional-order mathematical model (FOMM) by using normal and dysregulated bone remodeling of myeloma disease (MBD). For more precise performance model, derivatives have been used numerically. The FOMM is preliminarily designed focus on critical interactions between resorption or osteoclasts (OC) formation osteoblasts (OB). connections OC OB are represent...

The current research attempts to offer a novel method for solving fuzzy differential equations with initial conditions based on the use of feed-forward neural networks. First, the fuzzy differential equation is replaced by a system of ordinary differential equations. A trial solution of this system is written as a sum of two parts. The first part satisfies the initial condition and contains no ...

in this paper we intend to offer new numerical methods to solve the second-order fuzzy abel-volterraintegro-differential equations under the generalized $h$-differentiability. the existence and uniqueness of thesolution and convergence of the proposed methods are proved in details and the efficiency of the methods is illustrated through a numerical example.

In the present paper using homotopy analysis method (HAM), we approximate a special case of fuzzy integral equations. The fuzzy integral and integro-differential equations have a wide range of applications in science and engineering. In this paper HAM can be to find the exact solution or an approximate solution of the problem. Within this paper the HAM is used to obtain A series solution of int...

The basic ideas of semi-implicit time differencing are reviewed, including analytical results not widely referenced in the meteorological literature. It is shown that solving the resulting implicit equations by simple fixed-point iteration requires a relatively small time step to guarantee convergence, thus defeating the purpose of the semiimplicit method. In contrast, classical iteration metho...

The focus of this paper is to clarify the concepts of solutions of linear equations in interval, probabilistic, and fuzzy sets setting for real world tasks. There is a fundamental difference between formal definitions of the solutions and physically meaningful concepts of solution in applied tasks, when equations have uncertain components. For instance, a formal definition of the solution in te...