Originally, the revolutionary theory of smarandache notions was born as a paradoxist movement that challenged the status quo of existing mathematics. Prior to discussing fuzzy differential equations and integral equations and. Pdf this paper deals with the solutions of fuzzy fredholm integral equations using neural networks. Solving linear fredholm fuzzy integral equations system by. Finally in section 4, we apply the proposed method by an example to show the simplicity and e.
Solving a system of fuzzy integral equations by an analytic. If gx is a fuzzy function these equation may only possess fuzzy solution. Computational methods for solving linear fuzzy volterra integral equation. The iterated galerkin method for integral equations of the. 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.
Numerical solution of interval and fuzzy system of linear. Method of successive approximations for fredholm ie s e i r e s n n a m u e n 2. 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. Fuzzy fredholm integral equation 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. 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. Solution of fuzzy singular integral equation with abels type kernel. Method for solving fuzzy integro differential equation by. Fredholm integral equations in a fredholm integral equation the limits of integration are.
Pdf solving linear fredholm fuzzy integral equations of the. One of them solves differential equations using zadehs extension principle buckleyfeuring 30, while another approach interprets fuzzy differential equations through differential inclusions. This algorithm is implemented on some numerical examples by. In this paper the substantiation of the averaging method for fuzzy integral equation using the second approach is considered. Wu and ma 28 investigated the fuzzy fredholm integral equation of the second kind, which is one of the first applications of fuzzy integration. Pdf in this paper, a numerical procedure for solving fuzzy fredholm integral equations of the second kind fies with arbitrary kernels have been. Spectral method for solving fuzzy volterra integral equations. In fact, as we will see, many problems can be formulated equivalently as either a differential or an integral equation. Request pdf fuzzy integral equations we present two solution methods for fuzzy integral equations. This paper, about the solution of fuzzy volterra integral equation of fuzzy volterra integral equation of second kind fvie2 using spectral method is discussed. Adomian decomposition method homotopy analysis method. Pdf numerical solution of fuzzy integral equations researchgate. Altaie department of computer engineering and information technology, university of technology, baghdadiraq. On global existence of solution of nonlinear integral equations with.
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. Theory and numerical solution of volterra functional integral. Integral equation fuzzy number classical solution fredholm integral equation interval arithmetic these keywords were added by machine and not by the authors. Analytical and numerical methods for solving linear fuzzy volterra integral equation of the second kind by jihan tahsin abdel rahim hamaydi supervised prof. Chapter two includes existence of solutions of linear integral equations using adomain decomposition. A method for solving fuzzy fredholm integral equations of the. On the existence of a fuzzy integral equation of urysohnvolterra type. 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. If ft is a crisp function then the solutions of eqs. In this thesis, some analytical and numerical methods for solving fuzzy fredholm integral equation of the second kind will be investigated. The book is mainly oriented towards the theory of compact integral operators, partial differential operators and boundary value problems. It provides a complete treatment of numerous transform techniques fourier, laplace, mellin, hankel, hilbert.
Fuzzy volterra integral equation the fuzzy volterra integral equations of the second kind fvie2 is 24, 0 1. Application of fuzzy laplace transforms for solving fuzzy. Since it is difficult to solve fuzzy fredholm integral equations. Fuzzy linear systems have recently been studied by a good number of authors but only a few of them are mentioned here. 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. Solution of fuzzy volterra integral equations in a. Also, the fuzzy integral equations have been studied by several authors, 14, 15. Section 5 and 6 describe an experiment pertaining to syllableproximity evaluation using the fuzzy integrationbased aggregation. Moreover, some different valid methods for solving this kind of equations have been developed. 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. M n introduce the following definitions concerning the operators in the vector. 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.
Solving a system of fuzzy integral equations by an. Mt5802 integral equations introduction integral equations occur in a variety of applications, often being obtained from a differential equation. Differential equations department of mathematics, hkust. 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. Comparison of accurate solutions of nonlinear hammerstein fuzzy.
Fuzzy fredholm integral equation of the second kind is one of the main fuzzy equations addressed by many researchers. Averaging for fuzzy differential equations pdf paperity. Numerical solution of linear integral equations system using. In this paper, we have studied a fuzzy fractional differential equation and presented its solution using zadehs extension principle. Section 4, we illustrate algorithm by solving some numerical examples. 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. 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.
Then three cases for fvie2 are searched to solve them. The parametric form of fuzzy driving term is applied for fvie2. 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. 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. Wed like to understand how you use our websites in order to improve them.
Solving fuzzy fractional differential equations using zadehs. 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. A survey on solution methods for integral equations. Fuzzy integral equations and strong fuzzy henstock integrals. Naji qatanani abstract integral equations, in general, play a very important role in engineering and technology due to their wide range of applications. A method for solving fuzzy fredholm integral equations of the second kind m. Numerical solution of fuzzy fredholm integral equations of the second kind using bernstein polynomials sarmad a.
Solving fuzzy integral equations of the second kind by fuzzy. Bounded solutions for fuzzy integral equations of fractional. 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. Some numerical methods for fuzzy integral equations illustrated by3 using iterative method to the fuzzy function, also 5 used. We define an operator l as a map function from the vector space m to the vector space n. Solving fuzzy nonlinear volterrafredholm integral equations by. Recently the setvalued and fuzzy integral equations and inclusions began to be considered 614. Finally, an algorithm is presented to solve the fuzzy integral equation by using the trapezoidal rule. Solution of fuzzy volterra integral equations in a bernstein. Easily share your publications and get them in front of issuus. These proposed methods are used to solve a ham merstein integral equation by reducing to a system of nonlinear algebraic equations. It also contains elegant analytical and numerical methods, and an important topic of the variational principles. Solving a system of fuzzy integral equations by an analytic method.
Numerical solutions to fuzzy differential and integral equations, fuzzy sets and systems, 106 1999, pp. Volume 108, issue 2, 1 december 1999, pages 193200. Issuu is a digital publishing platform that makes it simple to publish magazines, catalogs, newspapers, books, and more online. Recently, bede introduced a strongly generalized di. Both solution methods are applied to two procedures for solving the crisp problem. 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. Section 7 provides a brief summary of the conclusions. This process is experimental and the keywords may be updated as the learning algorithm improves. In this book, we study the subject of smarandache fuzzy algebra. Abstract in this paper, a numerical method is given for solving fuzzy fredholm integral equations of the. A read is counted each time someone views a publication summary such as the title, abstract, and list of authors, clicks on a figure, or views or downloads the fulltext. However, if y is a fuzzy function then this equation may only possess fuzzy solutions.
Analytical and numerical methods for solving linear fuzzy. So, in this special issue, we intend to consider the numerical methods to solve fuzzy integral equations and the related topics with real applications. Particularly important examples of integral transforms include the fourier transform and the laplace transform, which we now. 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. This classifications are considered based on the sign of. 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. 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. The theory of integral equations ie is exposed in the framework of hilbert spaces. That is why different ideas and methods to solve fuzzy differential equations have been developed. Fuzzy differential equations and applications for engineers. Numerical solution of fuzzy fredholm integral equations of. 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.
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. Bozorgmanesh3 1,2department of mathematics, islamic azad university, iran email. Fredholm integral equations are related to boundaryvalue problems for di. Preliminaries let conv r n be a set of all nonempty convex compact subsets of the.
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