فهرس المقالات Fuzzy differential

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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 أکثر

  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. تفاصيل المقالة
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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 أکثر

  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.  تفاصيل المقالة
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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 أکثر

  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. تفاصيل المقالة
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  4 - تحلیل پایداری معادلات دیفرانسیل فازی ضربه‌ای دارای حالت تاخیری محدود
  داود ناصح ناصر پریز علی وحیدیان کامیاد
  در این مقاله معیارهایی برای بررسی پایداری دستگاه معادلات دیفرانسیل فازی ضربه­ای دارای تاخیر محدود در حالت ارائه می­گردد. ابتدا، قضیه مقایسه جدیدی برای کرانداری پاسخ سیستم دیفرانسیل فازی در قیاس با سیستم دیفرانسیل معمولی تعینی در فضای N بعدی بر اساس مفهوم توابع غ أکثر

  در این مقاله معیارهایی برای بررسی پایداری دستگاه معادلات دیفرانسیل فازی ضربه­ای دارای تاخیر محدود در حالت ارائه می­گردد. ابتدا، قضیه مقایسه جدیدی برای کرانداری پاسخ سیستم دیفرانسیل فازی در قیاس با سیستم دیفرانسیل معمولی تعینی در فضای N بعدی بر اساس مفهوم توابع غیرنزولی شبه یکنوای فوقانی بیان می­گردد؛ همچنین، برای تحلیل پایداری سیستم­های دینامیکی فازی، توابع شبه لیاپانوف برداری تعریف می­گردند. سپس با استفاده از این توابع برداری شبه لیاپانوف به همراه قضیه مقایسه جدیدی که مطرح شده است، برخی قضایا برای بررسی انواع مفاهیم پایداری (پایداری نهایی، پایداری مجانبی، پایداری قوی و پایداری یکنواخت) برای سیستم دیفرانسیل فازی ضربه­ای دارای حالت تاخیردار مطرح می­شوند. علاوه بر آن، قضایای پایداری کاربردی بر حسب دو معیار ارائه شده و به اثبات می­رسند. در انتها مثالی روشنگر برای نحوه بکارگیری قضایای پایداری مطرح و پایداری یک سیستم دیفرانسیل فازی دارای تاخیر بررسی می­گردد. تفاصيل المقالة
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  5 - 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 أکثر

  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. تفاصيل المقالة
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  6 - 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 أکثر

  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. تفاصيل المقالة
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  7 - 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 أکثر

  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. تفاصيل المقالة
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  8 - 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 أکثر

  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.‎ تفاصيل المقالة
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  9 - 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 أکثر

  ‎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.‎ تفاصيل المقالة
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  10 - Numerical solution of hybrid fuzzy differential equations by fuzzy neural network
  M. Othadi M. Mosleh
  The hybrid fuzzy differential equations have a wide range of applications in science and engineering. We consider the problem of nding their numerical solutions by using a novel hybrid method based on fuzzy neural network. Here neural network is considered as a part of أکثر

  The hybrid fuzzy differential equations have a wide range of applications in science and engineering. We consider the problem of nding their numerical solutions by using a novel hybrid method based on fuzzy neural network. Here neural network is considered as a part of large eld called neural computing or soft computing. The proposed algorithm is illustrated by numerical examples and the results obtained using the scheme presented here agree well with the analytical solutions. تفاصيل المقالة
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  11 - 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 أکثر

  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.‎ تفاصيل المقالة
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  12 - 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 أکثر

  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. تفاصيل المقالة
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  13 - 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 أکثر

  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 تفاصيل المقالة
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  14 - 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. أکثر

  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. تفاصيل المقالة
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  15 - Mathematical Modeling of Cancer Cells and Chemotherapy Protocol Dealing Optimization Using Fuzzy Differential Equations And Lypunov Stability Criterion
  Hadi Abbasnejad
  Mathematical models can simulate the growth and proliferation of cells in the interaction with healthy cells, the immune system and measure the toxicity of drug and its effects on healthy tissue pay. One of the main goals of modeling the structure and growth of cancer c أکثر

  Mathematical models can simulate the growth and proliferation of cells in the interaction with healthy cells, the immune system and measure the toxicity of drug and its effects on healthy tissue pay. One of the main goals of modeling the structure and growth of cancer cells is to find a control model suitable for administration among patients. In this study, a new mathematical model is designed to describe the changes in different phases of the cycle T cell proliferation, the population of immune cells, the proposed concentration of drug toxicity and treatment using differential equation and fuzzy Lyapunov stability, an optimal treatment protocol. One feature to consider is the rate of clearance of the drug in the body. تفاصيل المقالة
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  16 - A Method for Solving Linear Systems of Fuzzy Differential Equations under Generalized Hukuhara Differentiability
  Mehran Chehlabi Masuod Salehi Sarvestani
  10.30495/fomj.2023.1987990.1090
  The paper proposes a procedure for solving a linear system of fuzzy differential equations from the point of view of the generalized Hukuhara derivative. First, the method is based on two functions of half-length and midpoint of fuzzy numbers and next it is implemented أکثر

  The paper proposes a procedure for solving a linear system of fuzzy differential equations from the point of view of the generalized Hukuhara derivative. First, the method is based on two functions of half-length and midpoint of fuzzy numbers and next it is implemented on the problem in two separate cases of generalized Hukuhara differentiability, in details. Two numerical examples are given to clarify the practical application of the results. تفاصيل المقالة
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  17 - 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 أکثر

  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. تفاصيل المقالة
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  18 - The Full Averaging of Fuzzy Differential Inclusions
  Natalia Skripnik
  In this paper the substantiation of the method of full averaging for fuzzy differential inclusions is considered. These results generalize the results of [17, 20] for differential inclusions with Hukuhara derivative and of [18] for fuzzy differential equations.

  In this paper the substantiation of the method of full averaging for fuzzy differential inclusions is considered. These results generalize the results of [17, 20] for differential inclusions with Hukuhara derivative and of [18] for fuzzy differential equations. تفاصيل المقالة
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  19 - 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 أکثر

  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. تفاصيل المقالة
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  20 - 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 تفاصيل المقالة
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  21 - 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 أکثر

  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. تفاصيل المقالة
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  22 - 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 أکثر

  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. تفاصيل المقالة
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  23 - 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. تفاصيل المقالة
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  24 - 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 أکثر

  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. تفاصيل المقالة