Alireza Khastan

Periodic boundary value problems for first-order linear differential equations with uncertainty under generalized differentiability

We study the existence of solutions to a class of first-order linear fuzzy differential equations subject to periodic boundary conditions from the point of view of generalized differentiability. The objective of this paper is to show that fuzzy differential equations under generalized differentiability can be used in the study of periodic phenomena, by considering a combination of two types of derivatives with a switching point. We provide sufficient conditions which guarantee that the piecewise-defined solutions match adequately and illustrate, through some examples, the process of construction and calculation of solutions.

A new fuzzy approximation method to Cauchy problems by fuzzy transform

We present new numeric methods based on the first and second degree F-transform for solving the Cauchy problem. We show that they outperform the second order RungeKutta method especially when a right-hand function is oscillating and/or a solution is requested on a long interval. Moreover, a new numeric method to solve fuzzy initial value problem using the F-transform is presented. The suitability of the presented new methods is theoretically justified and illustrated on various examples.

Fuzzy delay differential equations under generalized differentiability

Abstract We interpret a fuzzy delay differential equation using the concept of generalized differentiability. In this setting, we prove the existence of two fuzzy solutions, each one corresponding to a different type of differentiability. Uniqueness is understood in the sense that the solutions considered do not have switching points. The applicability of the theoretical results is illustrated with some real world examples.

A new approach to fuzzy initial value problem

In this paper, we consider a high-order linear differential equation with fuzzy initial values. We present solution as a fuzzy set of real functions such that each real function satisfies the initial value problem by some membership degree. Also we propose a method based on properties of linear transformations to find the fuzzy solution. We find out the solution determined by our method coincides with one of the solutions obtained by the extension principle method. Some examples are presented to illustrate applicability of the proposed method.

Schauder fixed-point theorem in semilinear spaces and its application to fractional differential equations with uncertainty

We study the existence of solution for nonlinear fuzzy differential equations of fractional order involving the Riemann-Liouville derivative.

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.

A Numerical Method for Fuzzy Differential Equations and Hybrid Fuzzy Differential Equations

Numerical algorithms for solving first-order fuzzy differential equations and hybrid fuzzy differential equations have been investigated. Sufficient conditions for stability and convergence of the proposed algorithms are given, and their applicability is illustrated with some examples.

Conditioned weighted L-R approximations of fuzzy numbers

We compute the extended weighted L - R approximation of a given fuzzy number by a method based on general results in Hilbert spaces, the weighted average Euclidean distance being considered. The metric properties of the extended weighted L - R approximation of a fuzzy number are proved. We elaborate on a general method to study the existence, uniqueness and to calculate the L - R approximations of fuzzy numbers under the preservation of some parameters. We apply the results to find the weighted L - R approximations preserving ambiguity and value and respectively width in the general and unimodal case.

Relationship between Bede-Gal differentiable set-valued functions and their associated support functions

In this study, we adapt the concept of the Bede-Gal derivative, which was initially suggested for fuzzy number-valued functions, to set-valued functions. We use an example to demonstrate that this concept overcomes some of the shortcomings of the Hukuhara derivative.We prove some properties of Bede-Gal differentiable set-valued functions. We also study the relationship between a Bede-Gal differentiable set-valued function and its values support function, which we call the associated support function. We provide examples of set-valued functions that are not Bede-Gal differentiable whereas their associated support functions are differentiable. We also present some applications of the Bede-Gal derivative to solving set-valued differential equations.

New solutions for first order linear fuzzy difference equations

Abstract In this paper, we study the different formulations of fuzzy difference equation x n = w x n − 1 + q , where w , q are positive fuzzy numbers. Using a generalization of division for fuzzy numbers, we investigate the existence, uniqueness and global behavior of the solution.