Order Linear Fuzzy Differential Equations Research Articles

The BVP of a class of second order linear fuzzy differential equations is solved by Green function method under the concept of granular differentiability

The BVP of a class of second order linear fuzzy differential equations is solved by Green function method under the concept of granular differentiability

First order linear fuzzy differential equations with fuzzy variable coefficients

In this study, we investigate the first order linear fuzzy differential equations with fuzzy variable coefficients. Appearance of the multiplication of a fuzzy variable coefficient by an unknown fuzzy function in linear differential equations persuades us to employ the concept of the cross product of fuzzy numbers. Mentioned product overcomes to some difficulties we face to in the case of the usual product obtained by Zadeh’s extension principle. Under the cross product, we obtain the explicit fuzzy solutions for a fuzzy initial value problem applying the concept of the strongly generalized differentiability. Finally, some examples are given to illustrate the theoretical results. The obtained numerical results are compared with other approaches in the literature for similar parameters.

On solving fuzzy delay differential equation using bezier curves

In this article, we plan to use Bezier curves method to solve linear fuzzy delay differential equations. A Bezier curves method is presented and modified to solve fuzzy delay problems taking the advantages of the fuzzy set theory properties. The approximate solution with different degrees is compared to the exact solution to confirm that the linear fuzzy delay differential equations process is accurate and efficient. Numerical example is explained and analyzed involved first order linear fuzzy delay differential equations to demonstrate these proper features of this proposed problem.

Solutions of higher order linear fuzzy differential equations with interactive fuzzy values

In this study, we consider higher order linear differential equations with additional conditions (initial and/or boundary) given by interactive fuzzy numbers. The concept of interactivity arises from the notion of a joint possibility distribution (J). The proposed method for solving fuzzy differential equations is based on an extension of the classical solution via sup-J extension, which is a generalization of Zadeh's extension principle. We prove that under certain conditions, the solution via Zadeh's extension principle is equal to the convex hull of the solutions produced by the sup-J extension. We also show that the solutions based on the Fréchet derivatives of fuzzy functions coincide with the solutions obtained via the sup-J extension. All of the results are illustrated based on a 3rd order fuzzy boundary value problem.

On linear fuzzy differential equations by differential inclusions' approach

In this paper, we study first order linear fuzzy differential equations under differential inclusions and strongly generalized differentiability approaches. We present some new results on the relation between their solutions. Finally, some examples are given to illustrate our results.

Numerical solution of the first order linear fuzzy differential equations using He0s variational iteration method

Numerical solution of the first order linear fuzzy differential equations using He0s variational iteration method

On the solutions to first order linear fuzzy differential equations

In this paper, we study different formulations of first order linear fuzzy differential equations using the concept of generalized differentiability. We present sufficient conditions for the existence of solutions and obtain the general expression of these solutions, which exhibit different behavior. Some examples are given to illustrate our results.

On periodic solutions to first order linear fuzzy differential equations under differential inclusions’ approach

In this work, we study some properties of the solutions to first order linear fuzzy differential equations under differential inclusions’ approach. We show that the differential inclusions’ approach generally adapts better to some properties of the solutions to ordinary differential equations. Sufficient conditions for the solutions under this approach to be periodic and bounded are presented. We also give some examples to show the applicability of these results.

On the Ulam stability of first order linear fuzzy differential equations under generalized differentiability

In this paper we investigate, under some suitable conditions and generalized differentiability, the Ulam stability problems of three variants of first order linear fuzzy differential equations, respectively.

Numerical solution of first order linear fuzzy differential equations using Leapfrog method

This paper presents numerical solutions of first order linear fuzzy differential equations using Leapfrog method. The obtained discrete solutions are compared with single-term Haar wavelet series (STHWS) method (1). Error graphs and error calculation tables are presented to highlight the efficiency of the Leapfrog method. This method can be implemented in the digital computers and take any time of solutions.   h t y h t y h t y / 2     

Solution of the first order linear fuzzy differential equations by some reliable methods

Fuzzy differential equations are used in modeling problems in science and engineering. For instance, it is known that the knowledge of dynamical systems modeled by ordinary differential equations is often incomplete or vague. While, fuzzy differential equations represent a proper way to model dynamical systems under uncertainty and vagueness. In this paper, two methods for solving first order linear fuzzy differential equations under generalized differentiability are proposed and compared. These methods are variational iteration method (VIM) and Adomian decomposition method (ADM). The comparison of the exact solutions with solutions obtained by VIM and ADM are in details. The comparison shows that solutions are excellent agreement.

Variation of constant formula for first order fuzzy differential equations

In this paper, we study first order linear fuzzy differential equations by using the generalized differentiability concept and we present the general form of their solutions. We also correct and complete some previous results. Finally, some examples are given to illustrate our results.

First order linear fuzzy differential equations under generalized differentiability

First order linear fuzzy differential equations are investigated. We interpret a fuzzy differential equation by using the strongly generalized differentiability concept, because under this interpretation, we may obtain solutions which have a decreasing length of their support (which means a decreasing uncertainty). In several applications the behaviour of these solutions better reflects the behaviour of some real-world systems. Derivatives of the H-difference and the product of two functions are obtained and we provide solutions of first order linear fuzzy differential equations, using different versions of the variation of constants formula. Some examples show the rich behaviour of the solutions obtained.