فهرست مقالات fuzzy differential equation

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  1 - خواص ساختاری ضرب خارجی اعداد فازی و کاربردهای آن
  رباب علیخانی
  در حساب اعداد فازی، عمل ضرب و جمع بر اساس اصل توسیع زاده بنا نهاده شده است. این ضرب از دیدگاه نظری و عملی دارای چندین خاصیت غیرطبیعی است. برای غلبه بر چنین معایبی اخیراً یک عمل ضرب جدید با عنوان ضرب خارجی ارائه شده است. مزیت اصلی این ضرب این است که شکل اعداد فازی مثلثی چکیده کامل

  در حساب اعداد فازی، عمل ضرب و جمع بر اساس اصل توسیع زاده بنا نهاده شده است. این ضرب از دیدگاه نظری و عملی دارای چندین خاصیت غیرطبیعی است. برای غلبه بر چنین معایبی اخیراً یک عمل ضرب جدید با عنوان ضرب خارجی ارائه شده است. مزیت اصلی این ضرب این است که شکل اعداد فازی مثلثی و ذوزنقه‌ای تحت ضرب خارجی حفظ می‌شود و از دیدگاه محاسباتی خیلی کاربردی تر از ضرب معمولی است. بنابراین ضرب خارجی دو عدد فازی می‌تواند یک انتخاب دیگر به جای ضرب معمولی بدست آمده از اصل توسیع زاده، در مسائل کاربردی باشد. هدف این مقاله، ارائه‌ی فرمولی صریح برای ضرب خارجی اعداد فازی مثلثی بر اساس ضرب اسکالر اعداد فازی و سپس با استفاده از آن فرمولی برای طول ضرب خارجی دو عدد فازی مثلثی و مشتق ضرب خارجی دو تابع فازی مثلثی است. همچنین در این مقاله رابطه‌ی بین هسته ضرب خارجی و معمولی اعداد فازی بیان شده است. در نهایت، به عنوان یک کاربرد، مفهوم ضرب خارجی در معادلات دیفرانسیل خطی مرتبه‌ی اول با ضرایب متغییر فازی بکار برده شده و جواب‌های مثلثی آن تحت مشتق‌پذیری تعمیم یافته بدست آورده می‌شود.‌ چندین مثال برای بیان کارایی نتایج نظری و مقایسه با روش‎‌های پیشین آورده می‌شود. پرونده مقاله
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  2 - جواب تقریبی معادلات دیفرانسیل فازی مرتبه اول تحت مشتق تعمیم یافته
  توفیق الهویرنلو نازنین احمدی الهام احمدی
  در این تحقیق یک روش عددی به صورت تقریب قطعه­ای برای حل معادلات دیفرانسیل فازی معرفی می­گردد. در این روش جواب مساله با یک قطعه­ای چندجمله­ای از درجه سه در هر زیر بازه از جواب بیان می­گردد.مبنای روش، استفاده از بسط تیلور فازی تابع حول مقدار اولیه مساله چکیده کامل

  در این تحقیق یک روش عددی به صورت تقریب قطعه­ای برای حل معادلات دیفرانسیل فازی معرفی می­گردد. در این روش جواب مساله با یک قطعه­ای چندجمله­ای از درجه سه در هر زیر بازه از جواب بیان می­گردد.مبنای روش، استفاده از بسط تیلور فازی تابع حول مقدار اولیه مساله معادلات دیفرانسیل فازی می­باشد. وجود، یکتایی جواب و همچنین سرعت همگرایی روش تقریبی مورد بررسی قرار می­گیرد. همچنین نشان داده می­شود که روش معرفی شده در مقایسه با روش اویلر [1] برای حل معادلات دیفرانسیل فازی تحت مشتق تعمیم یافته دارای دقت بیشتری می­باشد.  پرونده مقاله
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  3 - حل عددی معادلات دیفرانسیل فازی مرتبه n با استفاده از روش آدامز- بشفورث
  نورالدین پرندین
  در این مقاله، روشی عددی برای حل معادلات دیفرانسیل مرتبه  پیشنهاد شده است. تاکنون روش­های زیادی برای حل معادلات دیفرانسیل فازی مرتبه اول، توسط محققین ارائه شده است. اما روش­های عددی کمتری نسبت به روش­های مرتبه اول، برای حل معادلات دیفرانسیل فازی مرتبه با چکیده کامل

  در این مقاله، روشی عددی برای حل معادلات دیفرانسیل مرتبه  پیشنهاد شده است. تاکنون روش­های زیادی برای حل معادلات دیفرانسیل فازی مرتبه اول، توسط محققین ارائه شده است. اما روش­های عددی کمتری نسبت به روش­های مرتبه اول، برای حل معادلات دیفرانسیل فازی مرتبه بالا پیشنهاد شده است. در این تحقیق، ابتداء معادله دیفرانسیل مرتبه n به دستگاهی از معادلات دیفرانسیل فازی مرتبه اول تبدیل می­شود، سپس از روش آدامز- بشفورث برای حل این دستگاه معادلات استفاده می­شود. نهایتاً با ارائه مثال­هایی، دقت روش سنجیده می­شود. پرونده مقاله
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  4 - Solving ‎S‎econd-Order Fuzzy Cauchy-Euler Initial Value Problems Under Generalized ‎Differentiability
  M. Chehlabi
  10.30495/ijim.2022.19222
  In this paper, we study a class of second-order fuzzy initial value problems that are known as the Cauchy-Euler differential equations, in the crisp case. This work begins by studying the structure of solution function in the crisp case and providing a requirement space چکیده کامل

  In this paper, we study a class of second-order fuzzy initial value problems that are known as the Cauchy-Euler differential equations, in the crisp case. This work begins by studying the structure of solution function in the crisp case and providing a requirement space of the generalized differentiable functions. In sequel, the process of production and construction of the solution formula are discussed, in details. Finally, the obtained formulas are applied and illustrated by solving some examples. پرونده مقاله
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  5 - A Numerical Algorithm for Solving Impulsive Fuzzy Initial Value Problem Based on Fuzzy Methods
  M. Dirbaz S. Abbasbandy
  In this paper, first the Newton’s divided difference interpolation method based on the gH difference on fuzzy data is introduced. Then the numerical methods entitled fuzzy Euler and modified fuzzy Euler are used to solve fuzzy impulsive initial value problem. More چکیده کامل

  In this paper, first the Newton’s divided difference interpolation method based on the gH difference on fuzzy data is introduced. Then the numerical methods entitled fuzzy Euler and modified fuzzy Euler are used to solve fuzzy impulsive initial value problem. Moreover the algorithms for the fuzzy impulsive initial value problem are explained and their local truncation errors are obtained in details. Finally, for more illustration some numerical examples are solved. پرونده مقاله
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  6 - Numerical Solution of Second-Order Hybrid Fuzzy Differential Equations by Generalized Differentiability
  N. Shahryari S. Abbasbandy
  In this research paper, a numerical method is presented for solving second-order hybrid fuzzy differential equations by using fuzzy Taylor expansion under generalized Hukuhara differentiability and also with convergence theorem. Also, the method is illustrated by solvin چکیده کامل

  In this research paper, a numerical method is presented for solving second-order hybrid fuzzy differential equations by using fuzzy Taylor expansion under generalized Hukuhara differentiability and also with convergence theorem. Also, the method is illustrated by solving several numerical examples. The final results showed that the solution of the second-order hybrid fuzzy differential equations. پرونده مقاله
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  7 - Solution of fuzzy differential equations
  M. Otadi M. Mosleh
  Hybrid system is a dynamic system that exhibits both continuous and discrete dynamic behavior‎. ‎The hybrid differential equations have a wide range of applications in science and engineering‎. ‎The hybrid systems are devoted to modeling‎, ‎desig چکیده کامل

  Hybrid system is a dynamic system that exhibits both continuous and discrete dynamic behavior‎. ‎The hybrid differential equations have a wide range of applications in science and engineering‎. ‎The hybrid systems are devoted to modeling‎, ‎design‎, ‎and validation of interactive systems of computer programs and continuous systems‎. ‎Hybrid fuzzy differential equations (HFDEs) is considered by Kim et al.‎ [11]. ‎In the present paper it is shown that the example presented by Kim et al‎. ‎in the Case I is not very accurate and in the Case II‎, ‎is incorrect.‎ ‎Namely‎, ‎the exact solution proposed by the authors in the Case II are not solutions of the given HFDE‎. ‎The correct exact solution is also presented here‎, ‎together with some results for characterizing solutions of FDEs under‎ ‎Hukuhara differentiability by an equivalent system of ODEs‎. ‎Then‎, ‎the homotopy analysis method (HAM) is applied to obtained the series solution of the HFDEs‎. ‎Finally‎, ‎we illustrate‎ ‎our approach by a numerical ‎example.‎ پرونده مقاله
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  8 - Approximate Solution of Fuzzy Fractional Differential Equations
  A. Panahi
  ‎In this paper we propose a method for computing approximations of solution of fuzzy fractional differential equations using fuzzy variational iteration method. Defining a fuzzy fractional derivative, we verify the utility of the method through two illustrative &lrm چکیده کامل

  ‎In this paper we propose a method for computing approximations of solution of fuzzy fractional differential equations using fuzzy variational iteration method. Defining a fuzzy fractional derivative, we verify the utility of the method through two illustrative ‎examples.‎ پرونده مقاله
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  9 - A Piecewise Approximate Method for Solving Second Order Fuzzy Differential Equations Under Generalized ‎Differentiability‎
  E. Ahmady N. Ahmady
  In this paper a numerical method for solving second order fuzzy differential equations under generalized differentiability is proposed. This method is based on the interpolating a solution by piecewise polynomial of degree 4 in the range of solution. Moreover we investi چکیده کامل

  In this paper a numerical method for solving second order fuzzy differential equations under generalized differentiability is proposed. This method is based on the interpolating a solution by piecewise polynomial of degree 4 in the range of solution. Moreover we investigate the existence, uniqueness and convergence of approximate solutions. Finally the accuracy of piecewise approximate method by some examples are ‎shown.‎ پرونده مقاله
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  10 - Generalized H-differentiability for solving second order linear fuzzy differential ‎equations
  P. Darabi S. Moloudzadeh‎ H. Khandani‎
  In this paper, a new approach for solving the second order fuzzy differential equations (FDE) with fuzzy initial value, under strongly generalized H-differentiability is presented. Solving first order fuzzy differential equations by extending 1-cut solution of the origi چکیده کامل

  In this paper, a new approach for solving the second order fuzzy differential equations (FDE) with fuzzy initial value, under strongly generalized H-differentiability is presented. Solving first order fuzzy differential equations by extending 1-cut solution of the original problem and solving fuzzy integro-differential equations has been investigated by some authors (see for example \cite{darabi1,TS}), but these methods have been done for fuzzy problems with triangular fuzzy initial value. Therefore by extending the r-cut solutions of the original problem we will obviate this deficiency. The presented idea is based on: if a second order fuzzy differential equation satisfy the Lipschitz condition then the initial value problem has a unique solution on a specific interval, therefore our main purpose is to present a method to find an interval on which the solution is ‎valid. پرونده مقاله
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  11 - Using finite difference method for solving linear two-point fuzzy boundary value problems based on extension principle
  Seyed Majid Alavi
  In this paper an efficient Algorithm based on Zadeh's extension principle has been investigated to approximate fuzzy solution of two-point fuzzy boundary value problems, with fuzzy boundary values. We use finite difference method in term of the upper bound and lower bou چکیده کامل

  In this paper an efficient Algorithm based on Zadeh's extension principle has been investigated to approximate fuzzy solution of two-point fuzzy boundary value problems, with fuzzy boundary values. We use finite difference method in term of the upper bound and lower bound of $r$- level of fuzzy boundary values. The proposed approach gives a linear system with crisp tridiagonal coefficients matrix. This linear system determines $r$-level of fuzzy solution at mesh points. By combining of this solutions, we obtain fuzzy solution of main problem at mesh points, approximately. Its applicabilityis illustrated by someexamples پرونده مقاله
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  12 - A novel existence and uniqueness theorem for solutions to FDEs driven by Lius process with weak Lipschitz coefficients
  S. Siah-Mansouri O. Solaymani Fard M. M. Gachpazan
  This paper we investigate the existence and uniqueness of solutions to fuzzydierential equations driven by Liu's process. For this, it is necessary to provideand prove a new existence and uniqueness theorem for fuzzy dierential equationsunder weak Lipschitz condition. چکیده کامل

  This paper we investigate the existence and uniqueness of solutions to fuzzydierential equations driven by Liu's process. For this, it is necessary to provideand prove a new existence and uniqueness theorem for fuzzy dierential equationsunder weak Lipschitz condition. Then the results allows us to considerand analyze solutions to a wide range of nonlinear fuzzy dierential equationsdriven by Liu's process. پرونده مقاله
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  13 - Solution of fuzzy differential equations under generalized differentiability by Adomian decomposition method
  ت. اللهویرانلو ل. جمشیدی
  Adomian decomposition method has been applied to solve many functional equations so far. In this article, we have used this method to solve the fuzzy differential equation under generalized differentiability. We interpret a fuzzy differential equation by using the stron چکیده کامل

  Adomian decomposition method has been applied to solve many functional equations so far. In this article, we have used this method to solve the fuzzy differential equation under generalized differentiability. We interpret a fuzzy differential equation by using the strongly generalized differentiability. Also one concrete application for ordinary fuzzy differential equation with fuzzy input data are given. پرونده مقاله
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  14 - Investigating and Improving the Uncertainty of Control Systems Using Fuzzy Differential Equations
  Fateme Arab
  Fuzzy differential equations have been widely used in recent years to model the uncertainty of mathematical models, and modeling has always been one of the practical ways to better understand and avoid wasting time in biological experiments. In this paper, in addition t چکیده کامل

  Fuzzy differential equations have been widely used in recent years to model the uncertainty of mathematical models, and modeling has always been one of the practical ways to better understand and avoid wasting time in biological experiments. In this paper, in addition to HIV biology, the necessity of using fuzzy systems in modeling has been investigated, the main methods in solving fuzzy differential equations according to the available sources have been introduced, and the advantages and disadvantages of each method have been explained. The second part of the article examines the results of modeling HIV-infected particles in an inaccurate environment using fuzzy logic in both analytical and numerical methods and simulates the model. پرونده مقاله
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  15 - Initial value problems for second order hybrid fuzzy differential equations
  M. Otadi
  Usage of fuzzy differential equations (FDEs) is a natural wayto model dynamical systems under possibilistic uncertainty. We consider second order hybrid fuzzy differentia

  Usage of fuzzy differential equations (FDEs) is a natural wayto model dynamical systems under possibilistic uncertainty. We consider second order hybrid fuzzy differentia پرونده مقاله
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  16 - Second order linear differential equations with generalized trapezoidal intuitionistic Fuzzy boundary value
  S. P. Mondal T. K. Roy
  In this paper the solution of a second order linear differential equations with intuitionistic fuzzy boundary value is described. It is discussed for two different cases: coefficientis positive crisp number and coefficient is negative crisp number. Here fuzzy numbers ar چکیده کامل

  In this paper the solution of a second order linear differential equations with intuitionistic fuzzy boundary value is described. It is discussed for two different cases: coefficientis positive crisp number and coefficient is negative crisp number. Here fuzzy numbers aretaken as generalized trapezoidal intutionistic fuzzy numbers (GTrIFNs). Further a numerical example is illustrated. پرونده مقاله
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  17 - Solution of the first order fuzzy differential equations with generalized differentiability
  L. Jamshidi T. Allahviranloo
  In this paper, we study first order linear fuzzy differential equations with fuzzycoefficient and initial value. We use the generalized differentiability concept and apply theexponent matrix to present the general form of their solutions. Finally, one example is givent چکیده کامل

  In this paper, we study first order linear fuzzy differential equations with fuzzycoefficient and initial value. We use the generalized differentiability concept and apply theexponent matrix to present the general form of their solutions. Finally, one example is givento illustrate our results. پرونده مقاله
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  18 - Initial Value ‎P‎roblems for Fourth-Order Fuzzy Differential Equations by Fuzzy Laplace ‎‎T‎ransform
  Hülya Gültekin Çitil
  This paper is on the solutions of fuzzy initial value problems for fourth-order fuzzy differential equations with positive and negative fuzzy coefficients by fuzzy Laplace transform. Examples are solved. Conclusions are given.

  This paper is on the solutions of fuzzy initial value problems for fourth-order fuzzy differential equations with positive and negative fuzzy coefficients by fuzzy Laplace transform. Examples are solved. Conclusions are given. پرونده مقاله
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  19 - APPLICATION OF DIFFERENTIAL TRANSFORM METHOD TO SOLVE HYBRID FUZZY DIFFERENTIAL EQUATIONS
  Mahmoud Paripour Homa Heidari Elahe Hajilou
  In this paper, we study the numerical solution of hybrid fuzzy differential equations by using differential transformation method (DTM). This is powerful method which consider the approximate solution of a nonlinear equation as an infinite series usually converging to t چکیده کامل

  In this paper, we study the numerical solution of hybrid fuzzy differential equations by using differential transformation method (DTM). This is powerful method which consider the approximate solution of a nonlinear equation as an infinite series usually converging to the accurate solution. Several numerical examples are given and by comparing the numerical results obtained from DTM and predictor corrector method (PCM), we have studied their accuracy. پرونده مقاله