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دسترسی آزاد مقاله
1 - روش تکرار تغییرات یانگ- لاپلاس کسری موضعی برای حل معادلات دیفرانسیل جزئی کسری موضعی
هما افراز جعفر صابری نجفیدر دهه های اخیر نظریه حساب کسری موضعی به طور موفقیت آمیزی برای توصیف و حل مسائل علوم پایه و مهندسی استفاده شده است .دراین پژوهش ، روش تکرارتغییرات یانگ لاپلاس کسری موضعی برای حل معادلات دیفرانسیل با مشتقات جزئی کسری موضعی روی مجموعه کانتور استفاده شده است. جواب‌های دقی چکیده کاملدر دهه های اخیر نظریه حساب کسری موضعی به طور موفقیت آمیزی برای توصیف و حل مسائل علوم پایه و مهندسی استفاده شده است .دراین پژوهش ، روش تکرارتغییرات یانگ لاپلاس کسری موضعی برای حل معادلات دیفرانسیل با مشتقات جزئی کسری موضعی روی مجموعه کانتور استفاده شده است. جواب‌های دقیق و تقریبی مشتق ناپذیر برای انواع معادلات دیفرانسیل خطی وغیرخطی بدست آمده است. نشان‌داده شده است که روش استفاده شده یک روش آسان و کارآمد برای اجرا در مسائل خطی وغیر خطی ناشی در علوم و مهندسی می‌باشد. دراین مقاله روی روش تکرارتغییرات یانگ لاپلاس کسری موضعی که از ترکیب روش تکرار تغییرات کسری موضعی وتبدیل یانگ لاپلاس بدست آمده است، تاکید شده است. بیشتر جواب‌های حاصل از این روش به صورت سری بدست می‌آیند که معمولا با سرعت به جواب‌های دقیق یا تقریبی همگرا می شوند. مثال های تشریحی نشان می دهدکه این روش قادر به کاهش حجم محاسبات نسبت به روش های کلاسیک موجود می باشد.. پرونده مقاله -
دسترسی آزاد مقاله
2 - حل عددی مدل کسری عفونت HIV در سلولهای CD4+T
محمد رضا دوستدار طیبه دمرچلی علیرضا وحیدیدر این مقاله، مدل کسری عفونت HIV در سلولهای CD4+T بررسی قرار میگیرد. در این مدل، مشتقات کسری در مفهوم کاپوتو در نظر گرفته میشوند. در این روش، دستگاه معادلات دیفرانسیل معمولی از مرتبه کسری به یک دستگاه معادلات جبری تبدیل میگردد که میتوان آن را با استفاده از یک روش عددی م چکیده کاملدر این مقاله، مدل کسری عفونت HIV در سلولهای CD4+T بررسی قرار میگیرد. در این مدل، مشتقات کسری در مفهوم کاپوتو در نظر گرفته میشوند. در این روش، دستگاه معادلات دیفرانسیل معمولی از مرتبه کسری به یک دستگاه معادلات جبری تبدیل میگردد که میتوان آن را با استفاده از یک روش عددی مناسب حل نمود. همچنین، در بحث آنالیز خطا، کران بالای خطا ارائه شده است. کارایی و دقت روش، با استفاده از یک نمونه عددی برای برخی مشتقات صحیح و کسری بررسی و برخی مقایسه ها و نتایج گزارش شده است. در این مقاله، مدل کسری عفونت HIV در سلولهای CD4+T بررسی قرار میگیرد. در این مدل، مشتقات کسری در مفهوم کاپوتو در نظر گرفته میشوند. در این روش، دستگاه معادلات دیفرانسیل معمولی از مرتبه کسری به یک دستگاه معادلات جبری تبدیل میگردد که میتوان آن را با استفاده از یک روش عددی مناسب حل نمود. همچنین، در بحث آنالیز خطا، کران بالای خطا ارائه شده است. کارایی و دقت روش، با استفاده از یک نمونه عددی برای برخی مشتقات صحیح و کسری بررسی و برخی مقایسه ها و نتایج گزارش شده است. پرونده مقاله -
دسترسی آزاد مقاله
3 - معرفی مشتق کوانتومی کسری فازی و خواص آن
ناصر میکائیل وند زهرا نوعی اقدممطالعه ی حساب کوانتومی یا کیو حساب توسط جکسون از اوایل قرن بیستم آغاز شد؛ امااخیرابه دلیل تقاضای زیادریاضیات، که محاسبات کوانتومی رامدل سازی می کند؛ باعث افزایش علاقه در این زمینه گردیده است.حساب کوانتومی یکی از علوم های کاربردی و بین رشته ای است که به دلیل داشتن ویژگی چکیده کاملمطالعه ی حساب کوانتومی یا کیو حساب توسط جکسون از اوایل قرن بیستم آغاز شد؛ امااخیرابه دلیل تقاضای زیادریاضیات، که محاسبات کوانتومی رامدل سازی می کند؛ باعث افزایش علاقه در این زمینه گردیده است.حساب کوانتومی یکی از علوم های کاربردی و بین رشته ای است که به دلیل داشتن ویژگی های خاص از جمله، تعریف مشتق بدون وجود حد باعث مزیتش نسبت به حساب معمولی شده است و کار با حساب کوانتومی از نظر عددی سریعتر و راحت تر از حساب استاندارد است. از آنجا که اکثر مسائل موجود در طبیعت منجر به مواجهه با معادلات فازی شامل مشتقاتی از مرتبه کسری می شوند؛ در این پژوهش بعد از معرفی مشتق کوانتومی (به اختصار کیومشتق) فازی بر مبنای تفاضل هاکوهارای تعمیم یافته، مشتق کوانتومی کاپوتوی کسری فازی و انتگرال کوانتومی (به اختصارکیوانتگرال) ریمن-لیوول کسری فازی رامعرفی می کنیم. سپس به بررسی قضایای اساسی و بیان تعاریف مهم در رابطه با کیومشتق کاپوتوی کسری فازی و کیوانتگرال ریمن-لیوول کسری فازی می پردازیم. که این نتایج دربسیاری ازبرنامه های کاربردی مانندفیزیک،نظریه کوانتومی،نظریه اعداد،مکانیک آماری وغیره رخ می دهد. پرونده مقاله -
دسترسی آزاد مقاله
4 - Approximate Solution of Fuzzy Fractional Differential Equations
A. Panahi‎In 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 کامل‎In 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 -
دسترسی آزاد مقاله
5 - Thermo-Viscoelastic Interaction Subjected to Fractional Fourier law with Three-Phase-Lag Effects
P Pal A Sur M KanoriaIn this paper, a new mathematical model of a Kelvin-Voigt type thermo-visco-elastic, infinite thermally conducting medium has been considered in the context of a new consideration of heat conduction having a non-local fractional order due to the presence of periodically چکیده کاملIn this paper, a new mathematical model of a Kelvin-Voigt type thermo-visco-elastic, infinite thermally conducting medium has been considered in the context of a new consideration of heat conduction having a non-local fractional order due to the presence of periodically varying heat sources. Three-phase-lag thermoelastic model, Green Naghdi models II and III (i.e., the models which predicts thermoelasticity without energy dissipation (TEWOED) and with energy dissipation (TEWED)) are employed to study the thermo-mechanical coupling, thermal and mechanical relaxation effects. In the absence of mechanical relaxations (viscous effect), the results for various generalized theories of thermoelasticity may be obtained as particular cases. The governing equations are expressed in Laplace-Fourier double transform domain. The inversion of the Fourier transform is carried out using residual calculus, where the poles of the integrand are obtained numerically in complex domain by using Laguerre's method and the inversion of the Laplace transform is done numerically using a method based on Fourier series expansion technique. Some comparisons have been shown in the form of the graphical representations to estimate the effect of the non-local fractional parameter and the effect of viscosity is also shown. پرونده مقاله -
دسترسی آزاد مقاله
6 - An extension of stochastic differential models by using the Grunwald-Letnikov fractional derivative
Mohammad Ali Jafari Narges MousaviyStochastic differential equations (SDEs) have been applied by engineers and economists because it can express the behavior of stochastic processes in compact expressions. In this paper, by using Grunwald-Letnikov fractional derivative, the stochastic differential model چکیده کاملStochastic differential equations (SDEs) have been applied by engineers and economists because it can express the behavior of stochastic processes in compact expressions. In this paper, by using Grunwald-Letnikov fractional derivative, the stochastic differential model is improved. Two numerical examples are presented to show efficiency of the proposed model. A numerical optimization approach based on least square approximation is applied to determine the order of the fractional derivative. Numerical examples show that the proposed model works better than the SDE to model stochastic processes with memory. پرونده مقاله -
دسترسی آزاد مقاله
7 - New Integral Transform for Solving Nonlinear Partial Di erential Equations of fractional order
A. Neamaty B. Agheli R. DarziIn this work, we have applied Elzaki transform and He's homotopy perturbation method to solvepartial di erential equation (PDEs) with time-fractional derivative. With help He's homotopy per-turbation, we can handle the nonlinear terms. Further, we have applied this sugg چکیده کاملIn this work, we have applied Elzaki transform and He's homotopy perturbation method to solvepartial di erential equation (PDEs) with time-fractional derivative. With help He's homotopy per-turbation, we can handle the nonlinear terms. Further, we have applied this suggested He's homotopyperturbation method in order to reformulate initial value problem. Some illustrative examples aregiven in order to show the ability and simplicity of the approach. All numerical calculations in thismanuscript were performed on a PC applying some programs written in Maple. پرونده مقاله -
دسترسی آزاد مقاله
8 - Fuzzy Ordinary and Fractional General Sigmoid Function Activated Neural Network Approximation
George AnastassiouHere we research the univariate fuzzy ordinary and fractional quantitative approximation of fuzzy real valued functions on a compact interval by quasi-interpolation general sigmoid activation function relied on fuzzy neural network operators. These approximations are de چکیده کاملHere we research the univariate fuzzy ordinary and fractional quantitative approximation of fuzzy real valued functions on a compact interval by quasi-interpolation general sigmoid activation function relied on fuzzy neural network operators. These approximations are derived by establishing fuzzy Jackson type inequalities involving the fuzzy moduli of continuity of the function, or of the right and left Caputo fuzzy fractional derivatives of the involved function. The approximations are fuzzy pointwise and fuzzy uniform. The related feed-forward fuzzy neural networks are with one hidden layer. We study in particular the fuzzy integer derivative and just fuzzy continuous cases. Our fuzzy fractional approximation result using higher order fuzzy differentiation converges better than in the fuzzy just continuous case. پرونده مقاله -
دسترسی آزاد مقاله
9 - New existence results for boundary value problems with integral conditions
Rahmat Darzi Roja Mahmoudi MatankolaeIn this paper, we investigate the existence and uniqueness of solution for fractionalboundary value problem (FBVP) with the integral boundary conditions. We use the contraction mapping principle and Krasnoselskii’s fixed point theorem to obtain some new existence چکیده کاملIn this paper, we investigate the existence and uniqueness of solution for fractionalboundary value problem (FBVP) with the integral boundary conditions. We use the contraction mapping principle and Krasnoselskii’s fixed point theorem to obtain some new existence and uniqueness results. پرونده مقاله -
دسترسی آزاد مقاله
10 - An Efficient Method for Solving the Fuzzy AH1N1/09 Influenza Model Using the Fuzzy Atangana-Baleanu-Caputo Fractional Derivative
Fatemeh BabakordiThe AH1N1/09 influenza virus is one of the most dangerous viruses that has greatly affected human life. As it is an unstable virus and new types of it with different features are created every year, its investigation is important. Various mathematical models have been p چکیده کاملThe AH1N1/09 influenza virus is one of the most dangerous viruses that has greatly affected human life. As it is an unstable virus and new types of it with different features are created every year, its investigation is important. Various mathematical models have been proposed to describe such diseases. In this paper, mathematical modeling in the form of fractional differential equations with the Atangana-Baleanu-Caputo (ABC) derivative and initial value is proposed to study this virus. Since the nature of the virus and how it affects the human body are ambiguous and imprecise, its fuzzy model is discussed. By using tools such as r-cut, generalized Hakuhara difference, ABC fractional derivative in fuzzy mode, and ABC-PI numerical method, the proposed model is solved numerically. At the end, a numerical example is provided to show the applicability of the method. پرونده مقاله -
دسترسی آزاد مقاله
11 - Application of the Lie Symmetry Analysis for second-order fractional differential equations
موسی ایلی جعفر بی آزار زینب آیتیObtaining analytical or numerical solution of fractional differential equations is one of the troublesome and challenging issue among mathematicians and engineers, specifically in recent years. The purpose of this paper Lie Symmetry method is developed to solve second-o چکیده کاملObtaining analytical or numerical solution of fractional differential equations is one of the troublesome and challenging issue among mathematicians and engineers, specifically in recent years. The purpose of this paper Lie Symmetry method is developed to solve second-order fractional differential equations, based on conformable fractional derivative. Some numerical examples are presented to illustrate the proposed approach. پرونده مقاله -
دسترسی آزاد مقاله
12 - A novel study on nonlinear fractional differential equations: general solution
موسی ایلی علی خوش کنارIn the present article, the Abel's technique has been developed to finding a general solution of the modified linear first-order ordinary differential equations in the sense of the truncated M-fractional derivative. By using proposed approach, a general solution of two چکیده کاملIn the present article, the Abel's technique has been developed to finding a general solution of the modified linear first-order ordinary differential equations in the sense of the truncated M-fractional derivative. By using proposed approach, a general solution of two well-recognized nonlinear first-order ordinary differential equations, Bernoulli and Riccati, in agreement with truncated M-fractional derivative have been obtained. For each equation, some examples are presented for satisfactory and efficiency of the proposed method. پرونده مقاله -
دسترسی آزاد مقاله
13 - Approximate solution of nonlinear fractional order model of HIV infection of CD4+T via Differential Quadrature Radial Basis Functions technique
کوکب چلمبری حمیده ابراهیمی زینب آیاتیIn this research, differential quadrature radial basis functions Method is performed to a fractional order model of HIV infection of CD4+T. Here, Caputo fractional derivative is used and it is approximated by forward finite difference method. Results have been compared چکیده کاملIn this research, differential quadrature radial basis functions Method is performed to a fractional order model of HIV infection of CD4+T. Here, Caputo fractional derivative is used and it is approximated by forward finite difference method. Results have been compared with the results of Laplace Adomian decomposition method (LADM), Laplace Adomian decomposition method-pade (LADM-pade), Runge-Kutta, Variational iteration method (VIM) and Variational iteration method-pade (VIM-Pade) for α_1=α_2=α_3 and residual functions have been plotted. And also approximate solutions of suggested method for different order of fractional derivatives have been shown. پرونده مقاله -
دسترسی آزاد مقاله
14 - Resonant solitons solutions to the time M-fractional Schrödinger equation
موسی ایلی علی خوش کنارIn this research the time M-fractional resonant nonlinear Schrödinger differential equation with different forms of nonlinearities, containing Kerr-law and parabolic-law has been studied. For this objective, the modified Kudryashov method and the sine-Gordon expans چکیده کاملIn this research the time M-fractional resonant nonlinear Schrödinger differential equation with different forms of nonlinearities, containing Kerr-law and parabolic-law has been studied. For this objective, the modified Kudryashov method and the sine-Gordon expansion approach have been implemented to retrieve a series of resonant solitons solutions for the abovementioned model. The prospective of the schemes in founding soliton solutions of nonlinear time-fractional equations in the truncated M-fractional derivative sense is confirmed. پرونده مقاله -
دسترسی آزاد مقاله
15 - A Chebyshev functions method for solving linear and nonlinear fractional differential equations based on Hilfer fractional derivative
M. H. Derakhshan A. AminataeiThe theory of derivatives and integrals of fractional in fractional calculus have found enormousapplications in mathematics, physics and engineering so for that reason we needan efficient and accurate computational method for the solution of fractional differential equa چکیده کاملThe theory of derivatives and integrals of fractional in fractional calculus have found enormousapplications in mathematics, physics and engineering so for that reason we needan efficient and accurate computational method for the solution of fractional differential equations.This paper presents a numerical method for solving a class of linear and nonlinear multi-order fractional differential equations with constant coefficients subject to initial conditions based on the fractional order Chebyshev functions that this function is defined as follows:\begin{equation*}\overline{T}_{i+1}^{\alpha}(x)=(4x^{\alpha}-2)\overline{T}_{i}^{\alpha}(x)\overline{T}_{i-1}^{\alpha}(x),\,i=0,1,2,\ldots,\end{equation*}where $\overline{T}_{i+1}^{\alpha}(x)$ can be defined by introducing the change of variable $x^{\alpha},\,\alpha>0$, on the shifted Chebyshevpolynomials of the first kind. This new method is an adaptation of collocationmethod in terms of truncated fractional order Chebyshev Series. To do this method, a new operational matrix of fractional order differential in the Hilfer sense for the fractional order Chebyshev functions is derived. By using this method we reduces such problems to those ofsolving a system of algebraic equations thus greatly simplifying the problem. At the end of this paper, several numerical experiments are given to demonstrate the efficiency and accuracy of the proposed method. پرونده مقاله -
دسترسی آزاد مقاله
16 - A New Implicit Finite Difference Method for Solving Time Fractional Diffusion Equation
elham afshariIn this paper, a time fractional diffusion equation on a finite domain is con- sidered. The time fractional diffusion equation is obtained from the standard diffusion equation by replacing the first order time derivative by a fractional derivative of order 0 < a< چکیده کاملIn this paper, a time fractional diffusion equation on a finite domain is con- sidered. The time fractional diffusion equation is obtained from the standard diffusion equation by replacing the first order time derivative by a fractional derivative of order 0 < a< 1 (in the Riemann-Liovill or Caputo sence). In equation that we consider the time fractional derivative is in the Caputo sense. We propose a new finite difference method for solving time fractional diffu- sion equation. In our method firstly, we transform the Caputo derivative into Riemann-Liovill derivative. The stability and convergence of this method are investigated by a Fourier analysis. We show that this method is uncondition- ally stable and convergent with the convergence order O( 2+h2), where t and h are time and space steps respectively. Finally, a numerical example is given that confirms our theoretical analysis and the behavior of error is examined to verify the order of convergence. پرونده مقاله -
دسترسی آزاد مقاله
17 - Cascade of Fractional Differential Equations and Generalized Mittag-Leffler Stability
Ndolane SeneThis paper address a new vision for the generalized Mittag-Leffler stability of the fractional differential equations. We mainly focus on a new method, consisting of decomposing a given fractional differential equation into a cascade of many sub-fractional differential چکیده کاملThis paper address a new vision for the generalized Mittag-Leffler stability of the fractional differential equations. We mainly focus on a new method, consisting of decomposing a given fractional differential equation into a cascade of many sub-fractional differential equations. And we propose a procedure for analyzing the generalized Mittag-Leffler stability for the given fractional differential equation using the generalized Mittag-Leffler input stability of the sub-fractional differential equations. In other words, we prove a cascade of fractional differential equations, which are generalized Mittag-Leffler input stables and governed by a fractional differential equation, which is generalized Mittag-Leffler stable, is generalized Mittag-Leffler stable. We give Illustrative examples to illustrate our main results. Note in our paper; we use the generalized fractional derivative in Caputo-Liouville sense. پرونده مقاله -
دسترسی آزاد مقاله
18 - Stability Analysis of Fractional Order Mathematical Model of Leukemia
Lahoucine BoujallalIn this paper, we propose a fractional order model of leukemia in terms of a system of ordinary differential equations with the Caputo derivative that provides convenience for initial conditions of the differential equations. Firstly, we prove the global existence, posi چکیده کاملIn this paper, we propose a fractional order model of leukemia in terms of a system of ordinary differential equations with the Caputo derivative that provides convenience for initial conditions of the differential equations. Firstly, we prove the global existence, positivity, and boundedness of solutions. The local stability properties of the equilibrium are obtained by using fractional Routh-Hurwitz stability criterion. Furthermore, a suitable Lyapunov functions are constructed to prove the global stability of equilibrium. Finally, numerical simulation of the model are presented to illustrate our theoretical results for different choices of fractional order of derivative α. Then, we can observe the impact of fractional derivative α on the evolution of the model states. پرونده مقاله -
دسترسی آزاد مقاله
19 - A Computational Approach for Fractal Mobile-Immobile Transport with Caputo-Fabrizio Fractional Derivative
Sadegh SadeghiThis paper deals with a spectral collocation method for the numerical solution of linear and nonlinear fractal Mobile/Immobile transport (FM/IT) model with Caputo-Fabrizio fractional derivative (C-F-FD). In the time direction, the finite difference procedure is used to چکیده کاملThis paper deals with a spectral collocation method for the numerical solution of linear and nonlinear fractal Mobile/Immobile transport (FM/IT) model with Caputo-Fabrizio fractional derivative (C-F-FD). In the time direction, the finite difference procedure is used to construct a semi-discrete problem and afterwards by applying a Chebyshev-spectral method, we obtain the approximate solution. The unconditional stability of the proposed method is proved which provides the theoretical basis of proposed method for solving the considered equation. Finally, some numerical experiments are included to clarify the efficiency and applicability of our proposed concepts in the sense of accuracy and convergence ratio. پرونده مقاله -
دسترسی آزاد مقاله
20 - HYBRID OF RATIONALIZED HAAR FUNCTIONS METHOD FOR SOLVING DIFFERENTIAL EQUATIONS OF FRACTIONAL ORDER
Y. Ordokhani N. RahimiAbstract. In this paper, we implement numerical solution of differential equations of frac- tional order based on hybrid functions consisting of block-pulse function and rationalized Haar functions. For this purpose, the properties of hybrid of rationalized Haar function چکیده کاملAbstract. In this paper, we implement numerical solution of differential equations of frac- tional order based on hybrid functions consisting of block-pulse function and rationalized Haar functions. For this purpose, the properties of hybrid of rationalized Haar functions are presented. In addition, the operational matrix of the fractional integration is obtained and is utilized to convert computation of fractional differential equations into some algebraic equa- tions. We evaluate application of present method by solving some numerical examples. پرونده مقاله
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