System Of Fuzzy Differential Equations Research Articles

Computationally semi-numerical technique for solving system of intuitionistic fuzzy differential equations with engineering applications

Some complex problems in science and engineering are modeled using fuzzy differential equations. Many fuzzy differential equations cannot be solved by using exact techniques because of the complexity of the problems mentioned. We utilize analytical techniques to solve a system of fuzzy differential equations because they are simple to use and frequently result in closed-form solutions. The Generalized Modified Adomian Decomposition Method is developed in this article to compute the analytical solution to the linear system of intuitionistic triangular fuzzy initial value problems. The starting values in this case are thought of as intuitionistic triangular fuzzy numbers. Engineering examples, such as the Brine Tanks Problem, are used to demonstrate the proposed approach and show how the series solution converges to the exact solution in closed form or in series. The corresponding graphs at different levels of uncertainty show the example’s numerical outcomes. The graphical representations further demonstrate the effectiveness and accuracy of the proposed method in comparison to Taylor’s approaches and the classical Decomposition method.

A Study of Fuzzy Methods for Solving System of Fuzzy Differential Equations

This paper is devoted to obtain an analytical solution for first-order fuzzy differential equations and system of fuzzy differential equations by different methods by considering the type of generalized Hukuhara differentiability of a solution and without embedding them to crisp equations. Moreover, the fuzzy solutions of a second-order fuzzy differential equation by considering the type of differentiability are obtained using reduction to a system of fuzzy differential equations. The effectiveness and efficiency of the approaches are illustrated by solving several practical examples such as Newton’s law of cooling, the mathematical models for the distribution of a drug in the human body and the fuzzy forced harmonic oscillator problem.

Fuzzy system model for gene expression

BackgroundThe theoretical information of a gene is contained in cell’s genetic materials, namely, DNA, mRNA and proteins. In the synthesis of functional gene products, this information can be expressed in mathematical way. AimIn this paper, a fuzzy approach is used to analyse of the behaviour of a gene expression in a cell. The main aim of the present study is to unravel the complexity of gene expression and develop the mathematical model which can be used for better insight of functional gene products. Subjects and methodsThe model for gene expression is obtained in terms of the system of fuzzy differential equations assuming that the transcription and translation processes are taking place in the cell. The Michaelis–Menten’s mechanism is incorporated in the model. ResultsThe analytic solution for crisp case as well as for fuzzy case is carried out. The sensitivity analysis is also performed and it is observed that the model is highly stable. ConclusionThe model for gene expression is obtained in terms of system of differential equations involving fuzzy initial values using geometric approach. The numerical results have been obtained for TJK16 strain of E.coli. The semi temporal concentrations profile of DNA, mRNA and protein are obtained and sensitivity analysis has been performed to study the variation in concentrations of DNA, mRNA and protein with respect to variation in transcription and translation rates.

A Novel Numerical Algorithm to Solve Systems of Fuzzy Differential Equations of Fractional and Integer Order Using Reproducing Hilbert Space Method

A Novel Numerical Algorithm to Solve Systems of Fuzzy Differential Equations of Fractional and Integer Order Using Reproducing Hilbert Space Method

On fuzzy solutions for heat equation based on generalized Hukuhara differentiability

In this paper a fuzzy heat equation with fuzzy initial values is considered. The concept of generalized Hukuhara differentiation is interpreted thoroughly in the univariate and multivariate cases, and also several properties for generalized Hukuhara differentiability are obtained on the topics, such as switching point, the univariate and multivariate fuzzy chain rules, fuzzy mean value theorem, among others. The objective of this paper is to prove the uniqueness of a solution for a fuzzy heat equation and show that a fuzzy heat equation can be modeled as two systems of fuzzy differential equations by considering the type of differentiability of solutions. Finally, some examples show the behavior of the solutions obtained.

Fuzzy neural network for solving a system of fuzzy differential equations

Fuzzy neural network (FNN) can be trained with crisp and fuzzy data. This paper presents a novel approach to solve system of fuzzy differential equations (SFDEs) with fuzzy initial values by applying the universal approximation method (UAM) through an artificial intelligence utility in a simple way. The model finds the approximated solution of SFDEs inside of its domain for the close enough neighborhood of the fuzzy initial points. We propose a learning algorithm from the cost function for adjusting of fuzzy weights. At the same time, some examples in engineering and economics are designed.

Averaging of fuzzy differential equations on a finite interval

We substantiate the applicability of total and partial averaging schemes to the investigation of systems of fuzzy differential equations with a small parameter.

Series Solution of the System of Fuzzy Differential Equations

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.

Variational Iteration Method for Solving n -th Order Fuzzy Differential Equations

In this paper, the variational iteration method (VIM) is employed to solve a system of fuzzy differential equations of first order. Since every ordinary fuzzy differential equations of higher order can be converted into a fuzzy system of the first order, this method can be used for solving n -th order fuzzy differential equations. Also the convergency of VIM for this system is proved. Finally to more illustrate several examples are solved.

Brief note on the variation of constants formula for fuzzy differential equations

This note gives a theory of state transition matrices for linear systems of fuzzy differential equations. This is used to give a fuzzy version of the classical variation of constants formula. A simple example of a time-independent control system is used to illustrate the methods. While similar problems to the crisp case arise for time-dependent systems, in time-independent cases the calculations are elementary solutions of eigenvalue–eigenvector problems. In particular, for nonnegative or nonpositive matrices, the problems at each level set, can easily be solved in MATLAB to give the level sets of the fuzzy solution.