Nonlinear Fuzzy Integro-differential Equations Research Articles

On Impulsive Nonlocal Nonlinear Fuzzy Integro-Differential Equations in Banach Space

The aim of this article is to investigate the existence, uniqueness and other qualitative properties of the solution of first-order nonlocal impulsive nonlinear fuzzy integro-differential equations in Banach space by using the concept of fuzzy numbers whose values are normal, upper semicontinuous, compact, and convex. The result is attained by utilizing a modified version of the Banach contraction principle. We offer an example as an application of the results.

The Fuzzy Differential Transform Method for the Solution of the System of Fuzzy Integro-Differential Equations Arising in Biological Model

This article deals with the implementation of fuzzy differential transform method for solving a system of nonlinear fuzzy integro-differential equations. This system appears in a model of biological species living together. Though the differential transform method is an iterative method, the current approach reduces this model to a set of nonlinear algebraic equations due to its delay terms. The basic definitions and theorems are first presented. The applicability and accuracy of the current methodologies have been demonstrated through the discussion of a few exemplary situations.

A modified reproducing Kernel Hilbert space method for solving fuzzy fractional integro-differential equations

The aim of this paper is to extend the application of the reproducing kernel Hilbert space method (RKHSM) to solve linear and non-linear fuzzy integro-differential equations of fractional order under Caputo's H-differentiability. The analytic and approximate solutions are given in series form in term of their parametric form in the space $W_2^2 [a,b] \bigoplus W_2^2 [a,b]$. Several examples are carried out to show the effectiveness and the absence of complexity of the proposed method

APPLICATION OF AN EFFECTIVE METHOD ON THE SYSTEM OF NONLINEAR FUZZY INTEGRO-DIFFERENTIAL EQUATIONS

In real world physical applications purpose, it is complicated to acquire an exact solution of fuzzy differential equations due to complexities in fuzzy arithmetic and therefore creating the need for the use of reliable and efficient techniques in the solution of fuzzy differential equations. The purpose of this research paper is to utilize the reliable analytic approach of homotopy perturbation Sumudu transform method for better understanding of systems of non-linear fuzzy integro-differential equations, while using the concept of fuzzy parameter in certain dynamical problems to remove the hurdles faced in numerical approach. These mathematical models are of great interest in engineering and physics. Some numerical examples are also given to demonstrate the efficiency and superiority of the method, followed by graphical representation of the comparison of exact and approximated solution by using Maple 2017

Study of Nonlinear Fuzzy Integro-differential Equations Using Mathematical Methods and Applications

Study of Nonlinear Fuzzy Integro-differential Equations Using Mathematical Methods and Applications

Sumudu Decomposition Method for Solving Fuzzy Integro-Differential Equations

Different results regarding different integro-differentials are usually not properly generalized, as they often do not satisfy some of the constraints. The field of fuzzy integro-differentials is very rich these days because of their different applications and functions in different physical phenomena. Solutions of linear fuzzy Volterra integro-differential equations (FVIDEs) are more generalized and have better applications. In this report, the Sumudu decomposition method (SDM) was used to find the solution to some linear and nonlinear fuzzy integro-differential equations (FIDEs). Some examples are given to show the validity of the presented method.

Application of Haar Wavelet Method for Solving the Nonlinear Fuzzy Integro-Differential Equations

Haar wavelet method (HWM) is an essential profitable method for settling the nonlinear Fuzzy Fredholm integro-differential equations (NFIDE). The proposed model converts the NFIDE into to nonlinear equations which tackle by the familiar Newton methods. The authors investigate the convergence of this method. Test problems are solved to show the accuracy of our method where the obtained numerical results are compared with Homotopy perturbation method (HPM) and the exact solutions. Graphical portrayals of the correct and obtained estimated arrangements illuminate the exactness of the methodology.

Iterative method for approximate solution of fuzzy integro-differential equations

In this paper, we interpret a nonlinear fuzzy Fredholm integro-differential equations by using the strongly generalized differentiability concept. Based on the parametric form of a fuzzy number, a fuzzy integro-differential equation converts to two systems of integro-differential equations in the crisp case. Also, we use the parametric form of fuzzy number, and an iterative approach for obtaining approximate solution for a class of nonlinear fuzzy Fredholm integro-differential equation of the second kind is proposed. This paper presents a method based on Newton–Cotes methods with positive coefficient. Then we obtain approximate solution of the nonlinear fuzzy integro-differential equations by an iterative approach.

A pertinent approach to solve nonlinear fuzzy integro-differential equations.

Fuzzy integro-differential equations is one of the important parts of fuzzy analysis theory that holds theoretical as well as applicable values in analytical dynamics and so an appropriate computational algorithm to solve them is in essence. In this article, we use parametric forms of fuzzy numbers and suggest an applicable approach for solving nonlinear fuzzy integro-differential equations using homotopy perturbation method. A clear and detailed description of the proposed method is provided. Our main objective is to illustrate that the construction of appropriate convex homotopy in a proper way leads to highly accurate solutions with less computational work. The efficiency of the approximation technique is expressed via stability and convergence analysis so as to guarantee the efficiency and performance of the methodology. Numerical examples are demonstrated to verify the convergence and it reveals the validity of the presented numerical technique. Numerical results are tabulated and examined by comparing the obtained approximate solutions with the known exact solutions. Graphical representations of the exact and acquired approximate fuzzy solutions clarify the accuracy of the approach.

NUMERICAL SOLUTIONS OF NONLINEAR FUZZY FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS OF THE SECOND KIND

In this paper, we use parametric form of fuzzy number, then aniterative approach for obtaining approximate solution for a classof nonlinear fuzzy Fredholmintegro-differential equation of the second kindis proposed. This paper presents a method based on Newton-Cotesmethods with positive coefficient. Then we obtain approximatesolution of the nonlinear fuzzy integro-differential equations by an iterativeapproach.

Existence, Uniqueness, and Characterization Theorems for Nonlinear Fuzzy Integrodifferential Equations of Volterra Type

Existence and uniqueness theorem are the tool which makes it possible for us to conclude that there exists only one solution to a given problem which satisfies a constraint condition. How does it work? Why is it the case? We believe it, but it would be interesting to see the main ideas behind this. To this end, in this paper, we investigate existence, uniqueness, and other properties of solutions of a certain nonlinear fuzzy Volterra integrodifferential equation under strongly generalized differentiability. The main tools employed in the analysis are based on the applications of the Banach fixed point theorem and a certain integral inequality with explicit estimate. Also, some results for characterizing solution by an equivalent system of crisp Volterra integrodifferential equations are presented. In this way, a new direction for the methods of analytic and approximate solutions is proposed.

Controllability of the nonlinear Fuzzy Integro-Differential Equations on EnN

In this paper we study the controllability for the nonlinear fuzzy integro-differential equations on Eⁿ N by using the concept of fuzzy number for dimension n whose values are normal, convex, semicontinuous and compactly supported surface in Rⁿ. Eⁿ N be the set of all fuzzy numbers in Rⁿ with edges having bases parallel to axis X₁, X₂, X₃…X n .

Existence and Uniqueness of Fuzzy Solutions for the nonlinear Fuzzy Integro-Differential Equation on EnN

In this paper we study the existence and uniqueness of fuzzy solutions for the nonlinear fuzzy integro-differential equations on <TEX>$E^{n}_{N}$</TEX> by using the concept of fuzzy number of dimension n whose values are normal, convex, upper semicontinuous and compactly supported surface in <TEX>$E^{n}_{N}$</TEX>. <TEX>$E^{n}_{N}$</TEX> be the set of all fuzzy numbers in <TEX>$R^{n}$</TEX> with edges having bases parallel to axis <TEX>$x_1$</TEX>, <TEX>$x_2$</TEX>, …, <TEX>$x_n$</TEX>.

Existence and uniqueness of fuzzy solution for the nonlinear fuzzy integrodifferential equations

In this paper, existence and uniqueness of fuzzy solution for the nonlinear fuzzy integrodifferential equations is established via Banach fixed-point analysis approach and using the fuzzy number whose values are normal, convex, upper semicontinuous and compactly supported interval in E N .