Intuitionistic Fuzzy Differential Equations Research Articles

On Extended Lr-Norm-Based Derivatives to Intuitionistic Fuzzy Sets

The study of differential equation theory has come a long way, with applications in various fields. In 1961, Zygmund and Calderón introduced the notion of derivatives to metric Lr, which proved to be better in applications than approximate derivatives. However, most of the studies available are on Fuzzy Set Theory. In view of this, intuitionistic fuzzy Lr-norm-based derivatives deserve study. In this study, the Lr-norm-based derivative for intuitionistic fuzzy number valued functions is introduced. Some of its basic properties are also discussed, along with numerical examples. The results obtained show that the proposed derivative is not dependent on the existence of the Hukuhara difference. Lastly, the Cauchy problem for the intuitionistic fuzzy differential equation is discussed.

An intuitionistic fuzzy differential equation approach for the lake water and sediment phosphorus model

Intuitionistic fuzzy sets cannot consider the degree of indeterminacy (i.e., the degree of hesitation). This study presents an intuitionistic fuzzy differential equation approach for the lake water and sediment phosphorus model. We examine the proposed model by assuming generalized trapezoidal intuitionistic fuzzy numbers for the initial condition. Feasible equilibrium points, along with their stability criteria, are evaluated. We describe the characteristics of intuitionistic fuzzy solutions and clarify the difference between strong and weak intuitionistic fuzzy solutions. Numerical simulations are performed in MATLAB to validate the model results.

A two-compartment drug concentration model using intuitionistic fuzzy sets

The intuitionistic fuzzy differential equation (IFDE) is a robust mathematical tool that can deal with problems arising from model uncertainties. Intuitionistic sets are generalized sets of fuzzy sets. They establish that IFDE comprises an intuitionistic number characterized by membership and non-membership functions. This paper deals with generalized Hukuhara derivatives for intuitionistic fuzzy-valued functions. A compartment drug concentration system has been described in a fuzzy, intuitionistic setting to get a more accurate mathematical model. The initial conditions of the proposed drug system are considered triangular intuitionistic fuzzy numbers. The proposed model’s critical points of stability analysis have been explored in an intuitionistic environment. All intuitionistic fuzzy solutions of the proposed system support robust solutions. All results and formulas are confirmed graphically and numerically by MATLAB software.

On the existence and uniqueness results for intuitionistic fuzzy partial differential equations

On the existence and uniqueness results for intuitionistic fuzzy partial differential equations

On the existence and uniqueness results for intuitionistic fuzzy partial differential equations

On the existence and uniqueness results for intuitionistic fuzzy partial differential equations

Semi-Analytical Scheme for Solving Intuitionistic Fuzzy System of Differential Equations

The aim of this article is to implement the Generalized Modified Adomian Decomposition Method to compute the semi-numerical solution of the linear system of intuitionistic fuzzy initial value problems. Here, we consider the initial values as generalized trapezoidal intuitionistic fuzzy numbers. The technique is applied to brine tanks problem and coupled mass spring systems.Theoretically, different approaches to solving a system of generalized trapezoidal intuitionistic fuzzy differential equations are discussed in this study under the presumption that the coefficients of the system of the differential equations are associated to generalized trapezoidal intuitionistic fuzzy numbers. The approximate results are compared with exact solutions which shows good efficiency. 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 existing semi-numerical methods in the literature.

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.

Convergence, Consistence, and Stability Analysis of One-Step Methods for First-Order Intuitionistic Fuzzy Differential Equations

In this work, we consider the initial value problems in intuitionistic fuzzy ordinary differential equations. The one-step method for approximating the solution of these problems has been defined. The convergence, consistency, and stability of the difference method for approximating the solution of intuitionistic fuzzy differential equations are studied, and the local truncation error is defined. The accuracy and efficiency of the proposed concept are illustrated by solving some numerical examples.

Integral boundary value problem for intuitionistic fuzzy delay partial differential equations

Integral boundary value problem for intuitionistic fuzzy delay partial differential equations

Approximate Solution of Intuitionistic Fuzzy Differential Equations with the Linear Differential Operator by the Homotopy Analysis Method

In this work, the purpose is to discuss the homotopy analysis method (HAM) for the use of intuitionistic fuzzy differential equations with the linear differential operator. Furthermore, a numerical example is presented to shed light on the capability of the present method, and the numerical results illustrated by adopting the homotopy perturbation method (HPM) are compared with the exact solution to ensure the validity of our outcomes.

Stability of intuitionistic fuzzy nonlinear fractional differential equations

In this paper, we study the existence and uniqueness results of solution for the intuitionistic fuzzy nonlinear fractional differential equations involving the Caputo concepts of fractional derivative. In addition, we establish essentially the Mittag-Leffler stability result for the intuitionistic fuzzy nonlinear fractional differential equations by giving some sufficient criteria to guarantee the stability of the zero solution. Finally, some examples are presented to illustrate the proposed stability theorem.

The Existence and Uniqueness of Intuitionistic Fuzzy Solutions for Intuitionistic Fuzzy Partial Functional Differential Equations

In this paper, we consider intuitionistic fuzzy partial functional differential equations with local and nonlocal initial conditions using the Banach fixed point theorem. A new complete intuitionistic fuzzy metric space is proposed to investigate the existence and uniqueness of intuitionistic fuzzy solutions for these problems. We use the level-set representation of intuitionistic fuzzy functions and define the solution to an intuitionistic fuzzy partial functional differential equation problem through a corresponding parametric problem and further develop theoretical results on the existence and uniqueness of the solution. An example is presented to illustrate the results with some numerical simulation for α-cuts of the intuitionistic fuzzy solutions: we give the representation of the surface of intuitionistic fuzzy solutions.

Narrow Metric Semi-linear Space of Intuitionistic Fuzzy Numbers: Application to AIDS Model

In this paper, we study two new binary operations, which are addition and scalar multiplication, for intuitionistic fuzzy numbers (IFNs). Thereafter, we introduce a semi-linear space for IFNs that it is called the narrow metric semi-linear space— $$L^{*}$$ . At the same time, we present a new type of intuitionistic fuzzy functions with a real domain and propose a number of concepts and properties for these functions such as geometric difference, geometric differentiability, derivative and integral. In addition, we give a model of initial value problem for intuitionistic fuzzy differential equations and present its application to an AIDS model. Some examples are given to illustrate the theoretical results.

Application of Runge-Kutta method for finding multiple numerical solutions to intuitionistic fuzzy differential equations

The present study is aimed to discuss multiple numerical solutions to first order ordinary differential equation which is intuitionistic fuzzy in nature, under the concept of generalised differentiability. The first order intuitionistic fuzzy differential equation which has been taken for the present study, is changed into four systems of ordinary differential equations by the (α, β)-cut representation of an intuitionistic fuzzy set. After the transformation, each system contains two pair of equations; one is for membership function and the other for non-membership function. Then, the fourth order Runge-Kutta method is applied in each pair and the competence of the method over Euler method and Modified Euler method are shown by solving a real time problem.

System of intuitionistic fuzzy differential equations with intuitionistic fuzzy initial values

System of intuitionistic fuzzy differential equations with intuitionistic fuzzy initial values

Solution of n-th order intuitionistic fuzzy differential equation by variational iteration method

Solution of n-th order intuitionistic fuzzy differential equation by variational iteration method

Initial Value Problem of Second Order Intuitionistic Fuzzy Ordinary Differential Equations

In this research paper, different cases of solution of the second order linear Intuitionistic Fuzzy Ordinary Differential Equations (IFODEs) are discussed. The initial conditions and the coefficients of differential equations are taken as the Generalized Trapezoidal Intuitionistic Fuzzy Numbers (GTrIFNs). The concept for finding the solution of second order linear homogeneous intuitionistic fuzzy ordinary differential equations is discussed in detail.

Approximate solution of intuitionistic fuzzy differential equations by using Picard's method

Approximate solution of intuitionistic fuzzy differential equations by using Picard's method

The Cauchy problem for intuitionistic fuzzy differential equations

The Cauchy problem for intuitionistic fuzzy differential equations

Solution of intuitionistic fuzzy fractional differential equations

Solution of intuitionistic fuzzy fractional differential equations