This classifications are considered based on the sign of. In order to complete the theory of fuzzy calculus and to transfer a fuzzy differential equation into a fuzzy integral equation, we 19, 20 have defined the strong fuzzy henstock integrals and discussed some of their properties and the controlled convergence theorem. Section 4, we illustrate algorithm by solving some numerical examples. An averaging result for fuzzy differential equations with a small parameter an averaging result for fuzzy differential equations with a small parameter 50 years sets with positive reach a survey 50 years sets with positive reach a survey. This paper, about the solution of fuzzy volterra integral equation of fuzzy volterra integral equation of second kind fvie2 using spectral method is discussed. A method for solving fuzzy fredholm integral equations of.
Finally in section 4, we apply the proposed method by an example to show the simplicity and e. Numerical solution of linear integral equations system using. Wed like to understand how you use our websites in order to improve them. Analytical and numerical methods for solving linear fuzzy. Solution of fuzzy singular integral equation with abels type kernel. Solving fuzzy nonlinear volterrafredholm integral equations by.
Abstract in this paper, we use new parametic formof fuzzy numbers and convert a system of fuzzy integral equations to two system of integral equations in crisp. Solution of fuzzy volterra integral equations in a bernstein. One of them solves differential equations using zadehs extension principle buckleyfeuring 30, while another approach interprets fuzzy differential equations through differential inclusions. The iterated galerkin method for integral equations of the second kind.
In this paper, a numerical procedure for solving fuzzy fredholm integral equations of the second kind fies with arbitrary kernels have been investigated and residual minimization method is given. Introduction integral equations appears in most applied areas and are as important as differential equations. Theory and numerical solution of volterra functional integral. Solving fuzzy integral equations of the second kind by fuzzy. In this thesis, some analytical and numerical methods for solving fuzzy fredholm integral equation of the second kind will be investigated. The classical fractional euler method has also been extended in the fuzzy setting in order to approximate the solutions of linear and nonlinear fuzzy fractional differential equations. Fuzzy integral equations and strong fuzzy henstock integrals shao, yabin and zhang, huanhuan, abstract and applied analysis, 20 existence of solutions of the wave equation involving the distributional henstockkurzweil integral liu, wei, lu, yueping, wang, ying, and ye, guoju, differential and integral equations, 2011. Some numerical methods for fuzzy integral equations illustrated by3 using iterative method to the fuzzy function, also 5 used.
Chapter two includes existence of solutions of linear integral equations using adomain decomposition. A survey on solution methods for integral equations. Solving linear fredholm fuzzy integral equations system by. Solving fuzzy fractional differential equations using zadehs. Spectral method for solving fuzzy volterra integral equations. A method for solving fuzzy fredholm integral equations of the second kind m. Abstract in this paper, a numerical method is given for solving fuzzy fredholm integral equations of the. Volume 108, issue 2, 1 december 1999, pages 193200. Hou,ad fuzzy integral equations john mordeson and william newman department of mathematicscomputer science, creighton unilersity, omaha, nebraska 68178 abstract we introduce a definition of the integral of a fuzzy valued function that is only slightly different from the usual one, yet that is more intuitive and that can be applied to a larger class of functions. The concept of fuzzy derivatives and fuzzy integration were studied in 11, 27 and then some generalization have been investigated in 10, 11, 24, 23. Method for solving fuzzy integro differential equation by. Its membership function is piecewise continuous of bounded support. A fuzzy linear system axb where a is a crisp matrix and b is a fuzzy number vector has been studied by friedman et al.
Wu and ma 28 investigated the fuzzy fredholm integral equation of the second kind, which is one of the first applications of fuzzy integration. Differential equations department of mathematics, hkust. Adomian decomposition method homotopy analysis method. Then three cases for fvie2 are searched to solve them. In this paper, we have studied a fuzzy fractional differential equation and presented its solution using zadehs extension principle. However, if y is a fuzzy function then this equation may only possess fuzzy solutions. Request pdf fuzzy integral equations we present two solution methods for fuzzy integral equations. These proposed methods are used to solve a ham merstein integral equation by reducing to a system of nonlinear algebraic equations. Using the parametric form of fuzzy numbers, the fuzzy linear fredholm integral equation of the second kind can be converted to a linear system of fredholm integral equations of the second kind in the crisp case. On the existence of a fuzzy integral equation of urysohnvolterra type.
Finally, an algorithm is presented to solve the fuzzy integral equation by using the trapezoidal rule. It provides a complete treatment of numerous transform techniques fourier, laplace, mellin, hankel, hilbert. Naji qatanani abstract integral equations, in general, play a very important role in engineering and technology due to their wide range of applications. Fuzzy fredholm integral equation of the second kind is one of the main fuzzy equations addressed by many researchers. Both solution methods are applied to two procedures for solving the crisp problem. If you want to learn differential equations, have a look at differential equations for engineers if your interests are matrices and elementary linear algebra, try matrix algebra for engineers if you want to learn vector calculus also known as multivariable calculus, or calculus three, you can sign up for vector calculus for engineers.
Altaie department of computer engineering and information technology, university of technology, baghdadiraq. Preliminaries let conv r n be a set of all nonempty convex compact subsets of the. The iterated galerkin method for integral equations of the. Fuzzy volterra integral equation the fuzzy volterra integral equations of the second kind fvie2 is 24, 0 1. Bounded solutions for fuzzy integral equations of fractional. Fuzzy differential equations and applications for engineers and scientists crc press book differential equations play a vital role in the modeling of physical and engineering problems, such as those in solid and fluid mechanics, viscoelasticity, biology, physics, and many other areas. Fredholm integral equations in a fredholm integral equation the limits of integration are. The reason for doing this is that it may make solution of the problem easier or, sometimes, enable us to prove fundamental results on the existence and uniqueness of the solution. Inspired by the work of 9, 10, in the present paper we aim to establish some sufficient conditions for the boundedness of every solution of fractional order fuzzy integral equations as well as certain fuzzy differential equations. Fuzzy integral equations and strong fuzzy henstock integrals.
In fact, as we will see, many problems can be formulated equivalently as either a differential or an integral equation. Since it is difficult to solve fuzzy fredholm integral equations. Application of fuzzy laplace transforms for solving fuzzy. Differential equations, difference equations and fuzzy logic in control of dynamic systems differential equations, difference equations and fuzzy logic in control of dynamic systems 3.
Comparison of accurate solutions of nonlinear hammerstein fuzzy. Pdf in this paper, a numerical procedure for solving fuzzy fredholm integral equations of the second kind fies with arbitrary kernels have been. Fuzzy fredholm integral equation of the second kind. This process is experimental and the keywords may be updated as the learning algorithm improves. The topic of fuzzy integral equations which has attracted growing interest for some time, in particular in relation to fuzzy control, has been developed in recent years. Particularly important examples of integral transforms include the fourier transform and the laplace transform, which we now. If ft is a crisp function then the solutions of eqs. Recently, bede introduced a strongly generalized di. Pdf numerical solution of fuzzy integral equations researchgate. Also, the fuzzy integral equations have been studied by several authors, 14, 15. Fuzzy integral equations of the second kind have attracted the attention of many scientists and researchers in recent years, due to their importance in applications, such as fuzzy control, fuzzy finance, approximate reasoning and economic systems 5. Fuzzy integral equations have attracted the attention of many scientists and researchers in recent years, due to their importance in applications, such as fuzzy control, fuzzy financial, approximate reasoning and economic system, etc.
Prior to discussing fuzzy differential equations and integral equations and. Integral equation fuzzy number classical solution fredholm integral equation interval arithmetic these keywords were added by machine and not by the authors. The book is mainly oriented towards the theory of compact integral operators, partial differential operators and boundary value problems. Solving a system of fuzzy integral equations by an analytic. In this paper we use fuzzy bunch functions to define every equation, and pay attention by finding a general formula of reduction to reduce fuzzy differential equations, and fuzzy volterra linear integral equations to fuzzy volterra linear. That is why different ideas and methods to solve fuzzy differential equations have been developed. Pdf this paper deals with the solutions of fuzzy fredholm integral equations using neural networks. So, in this special issue, we intend to consider the numerical methods to solve fuzzy integral equations and the related topics with real applications. Fuzzy differential equations and applications for engineers. The theory of integral equations ie is exposed in the framework of hilbert spaces. Section 5 and 6 describe an experiment pertaining to syllableproximity evaluation using the fuzzy integrationbased aggregation. Using the parametric form of fuzzy numbers, the fuzzy linear fredholm integral equation of the second kind can be converted to a linear system of fredholm integral equations of the second kind in the crisp. Kotsireasy june 2008 1 introduction integral equations arise naturally in applications, in many areas of mathematics, science and technology and have been studied extensively both at the theoretical and practical level. Bozorgmanesh3 1,2department of mathematics, islamic azad university, iran email.
In fact, obtaining the exact solutions of such fuzzy integral equations is not possible in all cases because of the inherited restrictions form application of fuzzy concepts in these problems. This algorithm is implemented on some numerical examples by. We define an operator l as a map function from the vector space m to the vector space n. Originally, the revolutionary theory of smarandache notions was born as a paradoxist movement that challenged the status quo of existing mathematics. The parametric form of fuzzy driving term is applied for fvie2. Solution of fuzzy volterra integral equations in a. Recently the setvalued and fuzzy integral equations and inclusions began to be considered 614. On global existence of solution of nonlinear integral equations with.
In this book, we study the subject of smarandache fuzzy algebra. Numerical solution of interval and fuzzy system of linear. Solving a system of fuzzy integral equations by an. Numerical solution of fuzzy fredholm integral equations of. Mt5802 integral equations introduction integral equations occur in a variety of applications, often being obtained from a differential equation. Fredholm integral equations are related to boundaryvalue problems for di. Fuzzy linear systems have recently been studied by a good number of authors but only a few of them are mentioned here. In 1992, liao 8 employed the basic ideas of the homotopy in topology to propose a general analytic method for nonlinear problems, namely homotopy analysis method. Issuu is a digital publishing platform that makes it simple to publish magazines, catalogs, newspapers, books, and more online. Numerical solution of fuzzy fredholm integral equations of the second kind using bernstein polynomials sarmad a. M n introduce the following definitions concerning the operators in the vector. Solving a system of fuzzy integral equations by an analytic method.
Moreover, some different valid methods for solving this kind of equations have been developed. Pdf solving linear fredholm fuzzy integral equations of the. Numerical solutions to fuzzy differential and integral equations, fuzzy sets and systems, 106 1999, pp. Section 7 provides a brief summary of the conclusions. In this paper the substantiation of the averaging method for fuzzy integral equation using the second approach is considered.
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